If[$VersionNumber>=2.,$Messages=OutputStream["",1],$Messages={}] BeginPackage["Transfor`m`"] Begin["`Private`"] (*Belegen von Module durch Block fr Versionen 1.?*) If[$VersionNumber<2.,Module=Block] (*!Achtung bei Erweiterungen: Am Dateiende sind vielleicht Modifikationen vorzunehmen!"*) TListe:=(Hyp`m`F[List1_List,List2_List,z_]:> Module[{HF,Ausgabe={},TFrage}, Hyp`m`Private`FRun=True; HF=(Hyp`m`F[List1,List2,z]/.Hyp`m`FOrdne); TFrage[Trans_,Perm1__,u,Perm2__,l]:= If[(HF/.Hyp`m`FPerm[Perm1,Global`u]/.Hyp`m`FPerm[Perm2,Global`l]/.Regel[Trans])=!= (HF/.Hyp`m`FPerm[Perm1,Global`u]/.Hyp`m`FPerm[Perm2,Global`l]), Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"u"],"FPerm"[Perm2,"l"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,u]:= If[(HF/.Hyp`m`FPerm[Perm1,Global`u]/.Regel[Trans])=!= (HF/.Hyp`m`FPerm[Perm1,Global`u]), Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"u"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,l]:= If[(HF/.Hyp`m`FPerm[Perm1,Global`l]/.Regel[Trans])=!= (HF/.Hyp`m`FPerm[Perm1,Global`l]), Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"l"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_,Perm1__,b]:= If[(HF/.Hyp`m`FPerm[Perm1,Global`b]/.Regel[Trans])=!= (HF/.Hyp`m`FPerm[Perm1,Global`b]), Ausgabe=Join[Ausgabe,{{"FPerm"[Perm1,"b"],StringJoin["T",ToString[Trans]]}}]]; TFrage[Trans_]:= If[(HF/.Regel[Trans])=!=HF, Ausgabe=Join[Ausgabe,{{StringJoin["T",ToString[Trans]]}}]]; TFrage[Global`rs01]; If[MemberQ[{{2,1},{3,2},{4,3},{5,4},{6,5},{7,6},{8,7},{9,8},{11,10}}, {Length[List1],Length[List2]}], Switch[{Length[HF[[1]]],Length[HF[[2]]]}, {2,1},TFrage[2103]; TFrage[2104]; TFrage[2106]; TFrage[2107]; TFrage[2110]; TFrage[2112]; TFrage[2131]; TFrage[2132]; TFrage[2133]; TFrage[2134]; TFrage[2135]; TFrage[2136]; TFrage[2137]; TFrage[2138]; TFrage[2139]; TFrage[2140]; TFrage[2141]; TFrage[2163]; TFrage[2191]; TFrage[2192], {3,2},TFrage[3204]; TFrage[3205]; TFrage[3206]; TFrage[3207]; TFrage[3217]; TFrage[3231]; TFrage[3231,1,3,2,u]; TFrage[3231,2,3,1,u]; TFrage[3231,2,1,l]; TFrage[3231,1,3,2,u,2,1,l]; TFrage[3231,2,3,1,u,2,1,l]; TFrage[3232]; TFrage[3232,1,3,2,u]; TFrage[3232,2,3,1,u]; TFrage[3232,2,1,3,u]; TFrage[3232,3,1,2,u]; TFrage[3232,3,2,1,u]; TFrage[3233]; TFrage[3233,1,3,2,u]; TFrage[3233,2,3,1,u]; TFrage[3233,2,1,3,u]; TFrage[3233,3,1,2,u]; TFrage[3233,3,2,1,u]; TFrage[3234]; TFrage[3234,1,3,2,u]; TFrage[3234,2,3,1,u]; TFrage[3234,2,1,l]; TFrage[3234,1,3,2,u,2,1,l]; TFrage[3234,2,3,1,u,2,1,l]; TFrage[3235]; TFrage[3235,1,3,2,u]; TFrage[3235,2,3,1,u]; TFrage[3235,2,1,l]; TFrage[3235,1,3,2,u,2,1,l]; TFrage[3235,2,3,1,u,2,1,l]; TFrage[3236]; TFrage[3237]; TFrage[3238]; TFrage[3238,1,3,2,u]; TFrage[3238,2,3,1,u]; TFrage[3238,2,1,3,u]; TFrage[3238,3,1,2,u]; TFrage[3238,3,2,1,u]; TFrage[3239]; TFrage[3240]; TFrage[3240,1,3,2,u]; TFrage[3240,2,3,1,u]; TFrage[3240,2,1,3,u]; TFrage[3240,3,1,2,u]; TFrage[3240,3,2,1,u]; TFrage[3261]; TFrage[3262]; TFrage[3263]; TFrage[3264]; TFrage[3267]; TFrage[3268], {4,3},TFrage[4301]; TFrage[4302]; TFrage[4303]; TFrage[4304]; TFrage[4306]; TFrage[4306,1,3,2,4,u]; TFrage[4306,1,4,2,3,u]; TFrage[4306,2,3,1,4,u]; TFrage[4306,2,4,1,3,u]; TFrage[4306,3,4,1,2,u]; TFrage[4306,1,3,2,l]; TFrage[4306,1,3,2,4,u,1,3,2,l]; TFrage[4306,1,4,2,3,u,1,3,2,l]; TFrage[4306,2,3,1,4,u,1,3,2,l]; TFrage[4306,2,4,1,3,u,1,3,2,l]; TFrage[4306,3,4,1,2,u,1,3,2,l]; TFrage[4306,2,1,3,l]; TFrage[4306,1,3,2,4,u,2,1,3,l]; TFrage[4306,1,4,2,3,u,2,1,3,l]; TFrage[4306,2,3,1,4,u,2,1,3,l]; TFrage[4306,2,4,1,3,u,2,1,3,l]; TFrage[4306,3,4,1,2,u,2,1,3,l]; TFrage[4306,2,3,1,l]; TFrage[4306,1,3,2,4,u,2,3,1,l]; TFrage[4306,1,4,2,3,u,2,3,1,l]; TFrage[4306,2,3,1,4,u,2,3,1,l]; TFrage[4306,2,4,1,3,u,2,3,1,l]; TFrage[4306,3,4,1,2,u,2,3,1,l]; TFrage[4306,3,1,2,l]; TFrage[4306,1,3,2,4,u,3,1,2,l]; TFrage[4306,1,4,2,3,u,3,1,2,l]; TFrage[4306,2,3,1,4,u,3,1,2,l]; TFrage[4306,2,4,1,3,u,3,1,2,l]; TFrage[4306,3,4,1,2,u,3,1,2,l]; TFrage[4306,3,2,1,l]; TFrage[4306,1,3,2,4,u,3,2,1,l]; TFrage[4306,1,4,2,3,u,3,2,1,l]; TFrage[4306,2,3,1,4,u,3,2,1,l]; TFrage[4306,2,4,1,3,u,3,2,1,l]; TFrage[4306,3,4,1,2,u,3,2,1,l]; TFrage[4309]; TFrage[4310]; If[Factor[z-1]===0&& ((Factor[HF[[1,1]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])|| (Factor[HF[[1,1]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])|| (Factor[HF[[1,1]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,1]]])|| (Factor[HF[[1,2]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])|| (Factor[HF[[1,2]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])|| (Factor[HF[[1,2]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,2]]])|| (Factor[HF[[1,3]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])|| (Factor[HF[[1,3]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])|| (Factor[HF[[1,3]]+1/2-HF[[1,4]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,3]]])|| (Factor[HF[[1,4]]+1/2-HF[[1,1]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])|| (Factor[HF[[1,4]]+1/2-HF[[1,2]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])|| (Factor[HF[[1,4]]+1/2-HF[[1,3]]]===0&&Hyp`m`Private`IntegerTest[2*HF[[1,4]]])), Print[""]; Print["\"T4312\" might be applicable."]; Print["Please, check for yourself!"]; ]; TFrage[4331]; If[Factor[z-1]===0, Print["If the series is nearly-poised of the first kind"]; Print["the transformation \"T4332\" might be applicable."]; TFrage[4332]; TFrage[4332,1,3,2,b]; TFrage[4332,2,3,1,b] ]; TFrage[4362]; TFrage[4391]; TFrage[4391,2,1,3,4,u]; TFrage[4391,3,1,2,4,u]; TFrage[4391,4,1,2,3,u]; TFrage[4391,2,1,3,l]; TFrage[4391,2,1,3,4,u,2,1,3,l]; TFrage[4391,3,1,2,4,u,2,1,3,l]; TFrage[4391,4,1,2,3,u,2,1,3,l]; TFrage[4391,1,3,2,l]; TFrage[4391,2,1,3,4,u,1,3,2,l]; TFrage[4391,3,1,2,4,u,1,3,2,l]; TFrage[4391,4,1,2,3,u,1,3,2,l]; TFrage[4391,2,3,1,l]; TFrage[4391,2,1,3,4,u,2,3,1,l]; TFrage[4391,3,1,2,4,u,2,3,1,l]; TFrage[4391,4,1,2,3,u,2,3,1,l]; TFrage[4391,3,2,1,l]; TFrage[4391,2,1,3,4,u,3,2,1,l]; TFrage[4391,3,1,2,4,u,3,2,1,l]; TFrage[4391,4,1,2,3,u,3,2,1,l]; TFrage[4391,3,1,2,l]; TFrage[4391,2,1,3,4,u,3,1,2,l]; TFrage[4391,3,1,2,4,u,3,1,2,l]; TFrage[4391,4,1,2,3,u,3,1,2,l], {5,4},TFrage[5401]; TFrage[5401,2,3,4,1,b]; TFrage[5401,1,3,4,2,b]; TFrage[5401,1,2,4,3,b]; TFrage[5402]; TFrage[5402,2,3,4,1,b]; TFrage[5402,1,3,4,2,b]; TFrage[5402,1,2,4,3,b]; If[Factor[z-1]===0&& (Hyp`m`Private`IntegerTest[HF[[1,1]]]|| Hyp`m`Private`IntegerTest[HF[[1,2]]]|| Hyp`m`Private`IntegerTest[HF[[1,3]]]|| Hyp`m`Private`IntegerTest[HF[[1,4]]]|| Hyp`m`Private`IntegerTest[HF[[1,5]]]), Print[""]; Print["\"T5403\" might be applicable."]; Print["Please, check for yourself!"]; ]; TFrage[5468], {6,5},TFrage[6501]; TFrage[6501,1,3,4,5,2,b]; TFrage[6501,1,2,4,5,3,b]; TFrage[6501,1,2,3,5,4,b]; TFrage[6531]; TFrage[6531,1,3,4,5,2,b]; TFrage[6531,1,2,4,5,3,b]; TFrage[6531,1,2,3,5,4,b]; TFrage[6532]; TFrage[6532,1,3,2,4,5,b]; TFrage[6532,1,4,2,3,5,b]; TFrage[6532,1,5,2,3,4,b]; TFrage[6533]; TFrage[6533,1,3,4,5,2,b]; TFrage[6533,1,2,4,5,3,b]; TFrage[6533,1,2,3,5,4,b]; TFrage[6534], {7,6},TFrage[7631]; TFrage[7632]; TFrage[7633]; TFrage[7633,1,2,3,5,4,6,b]; TFrage[7633,1,2,3,6,4,5,b]; TFrage[7633,1,2,4,5,3,6,b]; TFrage[7633,1,2,4,6,3,5,b]; TFrage[7633,1,2,5,6,3,4,b]; TFrage[7633,1,3,4,5,2,6,b]; TFrage[7633,1,3,4,6,2,5,b]; TFrage[7633,1,3,5,6,2,4,b]; TFrage[7633,1,4,5,6,2,3,b]; TFrage[7634]; TFrage[7635]; TFrage[7691]; TFrage[7692]; TFrage[7693]; TFrage[7694]; If[Factor[z-1]===0&& Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&& Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}], Print[""]; Print["The series is very well-poised. In addition to the transformations"]; Print["in the following list the transformations \"T7636\" and \"T7637\""]; Print["might be applicable."]; Print["Please, check for yourself!"]; ], {8,7},If[Factor[z+1]===0&& Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&& Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}], Print[""]; Print["The series is very well-poised. In addition to the transformations"]; Print["in the following list the transformations \"T8731\" or \"T8732\""]; Print["might be applicable. Please, check for yourself!"]; ], {9,8},TFrage[9831]; TFrage[9835]; TFrage[9835,1,2,3,4,5,6,8,7,b]; TFrage[9835,1,2,3,4,5,7,8,6,b]; TFrage[9835,1,2,3,4,6,7,8,5,b]; TFrage[9835,1,2,3,5,6,7,8,4,b]; TFrage[9835,1,2,4,5,6,7,8,3,b]; TFrage[9835,1,3,4,5,6,7,8,2,b]; TFrage[9891]; TFrage[9893]; If[Factor[z-1]===0&& Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&& Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}], Print[""]; Print["The series is very well-poised. In addition to the transformations"]; Print["in the following list the transformations \"T9832\", \"T9833\","]; Print["\"T9834\", \"T9837\", \"T9892\", or \"T9894\""]; Print["might be applicable. Please, check for yourself!"]; ]; Print[""]; Print["In addition to the transformations in the following"]; Print["list the \"split-poised\" transformation \"T9836\""]; Print["might be applicable. Please, check for yourself!"], {11,10},If[Factor[z-1]===0&& Factor[HF[[1,1]]-(HF[[1,2]])*2+2]===0&& Factor[Map[(1+HF[[1,1]]-#)&,Drop[HF[[1]],1]]-HF[[2]]]===Table[0,{Length[HF[[2]]]}], Print[""]; Print["The series is very well-poised. The transformations \"T111031\""]; Print["or \"T111032\" might be applicable. Please, check for yourself!"]; ]; ] ]; Hyp`m`Private`FRun=False; If[Ausgabe=!={}&&Ausgabe=!=HF, Print[""]; Print["Be sure to apply \"FOrdne\" before using the following information!"]]; Ausgabe ]); simplify[x_]:=(Simplify[x]/.Hyp`m`Expandq) Trs01:=(Hyp`m`F[List1_List,List2_List,1]:> Catch[ Module[{GesList,ii,iii,Var1,Var2,MinEl,POSX,NewList1={},NewList2={}, ProvList1=List1,ProvList2=List2,mList={},Ausgabe}, Ausgabe=Hyp`m`F[List1,List2,1]; If[(List2==={})||!(Length[List1]-Length[List2]===1), Throw[Ausgabe], GesList=ProvList2; For[ii=1,ii<=Length[GesList]&&Length[ProvList2]>1,ii++, Var2=ProvList1-GesList[[ii]]; Var1=Map[(IntegerQ[#]&&#>=0)&,Var2]; If[MemberQ[Var1,True], Var1=Var1/.True->1/.False->Indeterminate; Var2=Var2*Var1; Var2=Var2/.Indeterminate->Infinity; MinEl=Min[Var2]; mList=Join[mList,{MinEl}]; POSX=Hyp`m`Private`POS[Var2,MinEl]; {ProvList1,ProvList2,NewList1,NewList2}= Hyp`m`Private`PoisEliminate[ProvList1,ProvList2,NewList1,NewList2, ProvList1[[POSX]],GesList[[ii]]]; ] ]; Clear[ii]; If[Length[ProvList2]===1, Throw[1/Hyp`m`GAMMA[1-ProvList1[[1]]+ProvList1[[2]]]/ Hyp`m`GAMMA[ProvList2[[1]]-ProvList1[[2]]]* Hyp`m`GAMMA[1-ProvList1[[1]]]* Hyp`m`GAMMA[ProvList2[[1]]]* Product[Hyp`m`p[NewList2[[ii]]-ProvList1[[2]],mList[[ii]]],{ii,1,Length[NewList2]}]/ Product[Hyp`m`p[NewList2[[ii]],mList[[ii]]],{ii,1,Length[NewList2]}]* Hyp`m`F[Join[{1+ProvList1[[2]]-ProvList2[[1]],ProvList1[[2]]}, 1+ProvList1[[2]]-NewList2], Join[{1-ProvList1[[1]]+ProvList1[[2]]}, 1+ProvList1[[2]]-NewList1],1]], Throw[Hyp`m`F[List1,List2,1]] ]; ]]]); T2103:=(Hyp`m`F[{a_,b_},{c_},z_]:>(1-z)^(c-a-b)*Hyp`m`F[{c-a,c-b},{c},z]); T2104:=(Hyp`m`F[{a_,b_},{c_},z_]:>(1-z)^(-a)*Hyp`m`F[{a,c-b},{c},-z/(1-z)]); T2106:={Hyp`m`F[{a_,b_},{c_},z_]:>Hyp`m`p[c-b,-a]/ Hyp`m`p[c,-a]*(z)^(-a)* Hyp`m`F[{a,1+a-c},{b-c+1+a},-(1-z)/z]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{b_,a_},{c_},z_]:>Hyp`m`p[c-b,-a]/ Hyp`m`p[c,-a]*(z)^(-a)* Hyp`m`F[{a,1+a-c},{b-c+1+a},-(1-z)/z]/; Hyp`m`Private`IntegerTest[a]}; T2107:={Hyp`m`F[{a_,b_},{c_},z_]:>Hyp`m`p[c-b,-a]/ Hyp`m`p[c,-a]* Hyp`m`F[{a,b},{b-c+1+a},1-z]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{b_,a_},{c_},z_]:>Hyp`m`p[c-b,-a]/ Hyp`m`p[c,-a]* Hyp`m`F[{a,b},{b-c+1+a},1-z]/; Hyp`m`Private`IntegerTest[a]}; T2131:={Hyp`m`F[{c_,a_},{d_},z_]:>Hyp`m`F[{a,d-c},{1+a-c},1/(1-z)]/ (Hyp`m`p[d,-a])*(1-z)^(-a)* Hyp`m`p[c,-a]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{a_,c_},{d_},z_]:>Hyp`m`F[{a,d-c},{1+a-c},1/(1-z)]/ (Hyp`m`p[d,-a])*(1-z)^(-a)* Hyp`m`p[c,-a]/; Hyp`m`Private`IntegerTest[a]}; T3204:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:> Hyp`m`GAMMA[{e,d+e-(a+b+c)},{e-a,d+e-(b+c)}]* Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]); T3205:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:> Hyp`m`GAMMA[{d,e,d+e-(a+b+c)},{b,d+e-(a+b),d+e-(b+c)}]* Hyp`m`F[{d-b,e-b,d+e-(a+b+c)},{d+e-(a+b),d+e-(b+c)},1]); T3206:={Hyp`m`F[{b_,c_,a_},{d_,e_},1]:> Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{b_,a_,c_},{d_,e_},1]:> Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{a_,c_,b_},{d_,e_},1]:> Hyp`m`p[d+e-(b+c),-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,d-b,d-c},{d,d+e-(b+c)},1]/; Hyp`m`Private`IntegerTest[a]}; T3207:={Hyp`m`F[{b_,c_,a_},{d_,e_},1]:> Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{b_,a_,c_},{d_,e_},1]:> Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/; Hyp`m`Private`IntegerTest[a], Hyp`m`F[{a_,c_,b_},{d_,e_},1]:> Hyp`m`p[e-c,-a]/Hyp`m`p[e,-a]* Hyp`m`F[{a,c,d-b},{d,c+1+a-e},1]/; Hyp`m`Private`IntegerTest[a]}; T3239:=(Hyp`m`F[{a_,b_,c_},{d_,e_},z_]:> (1-z)^(-a)* Hyp`m`F[{(a/2),(a+1)/2,a+1-(b+c)}, {a+1-b,a+1-c},-4*z/(1-z)^2]/; Factor[a+1-b-d]===Factor[a+1-c-e]===0); T4301:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:> Hyp`m`p[{e-a,f-a},{e,f},-d]* Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)}, {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:> Hyp`m`p[{e-a,f-a},{e,f},-d]* Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)}, {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:> Hyp`m`p[{e-a,f-a},{e,f},-d]* Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)}, {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:> Hyp`m`p[{e-a,f-a},{e,f},-d]* Hyp`m`F[{d,a,(a+c+d+1)-(e+f),(a+b+d+1)-(e+f)}, {(a+b+c+d+1)-(e+f),(a+1+d)-e,(a+1+d)-f},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d]}; T4302:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:> Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]* Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:> Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]* Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:> Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]* Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:> Hyp`m`p[{a,e+f-(a+b),e+f-(a+c)},{e,f,e+f-(a+b+c)},-d]* Hyp`m`F[{d,e-a,f-a,e+f-(a+b+c)},{e+f-(a+b),e+f-(a+c),1+d-a},1]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d]}; T7631:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},z_]:> Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f)}, {a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f)}]* Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0&& (Hyp`m`Private`IntegerTest[a+1-b-c]||Hyp`m`Private`IntegerTest[d]||Hyp`m`Private`IntegerTest[e]||Hyp`m`Private`IntegerTest[f])); T7632:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},z_]:> Hyp`m`p[{a+1,a+1-(d+e)},{a+1-d,a+1-e},-f]* Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0&& Hyp`m`Private`IntegerTest[f]); T4303:={Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:> Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d}, {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b), (e+f)-(a+c),(e+f)-(a+d)},1]* Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)}, -d]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,b_,d_,c_},{e_,f_,g_},1]:> Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d}, {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b), (e+f)-(a+c),(e+f)-(a+d)},1]* Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)}, -d]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{a_,d_,c_,b_},{e_,f_,g_},1]:> Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d}, {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b), (e+f)-(a+c),(e+f)-(a+d)},1]* Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)}, -d]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d], Hyp`m`F[{d_,b_,c_,a_},{e_,f_,g_},1]:> Hyp`m`F[{(e+f)-(a+1),((e/2)+(f/2)+(1/2))-(a/2),f-a,e-a,b,c,d}, {((e/2)+(f/2))-((a/2)+(1/2)),e,f,(e+f)-(a+b), (e+f)-(a+c),(e+f)-(a+d)},1]* Hyp`m`p[{(e+f)-(a+b),(e+f)-(a+c)},{(e+f)-a,(e+f)-(a+b+c)}, -d]/; Factor[g-(a+b+c+d+1)+(e+f)]===0&& Hyp`m`Private`IntegerTest[d]}; T4304:={Hyp`m`F[{a_,b_,c_,g_},{d_,e_,f_},1] :> Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g}, {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]* Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g}, {(d/2)+(e/2)-(1/2)-(g/2), (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/; Factor[f-(a+b+c+g+1)+(d+e)]===0&& Hyp`m`Private`IntegerTest[g], Hyp`m`F[{a_,b_,g_,c_},{d_,e_,f_},1] :> Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g}, {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]* Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g}, {(d/2)+(e/2)-(1/2)-(g/2), (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/; Factor[f-(a+b+c+g+1)+(d+e)]===0&& Hyp`m`Private`IntegerTest[g], Hyp`m`F[{a_,g_,c_,b_},{d_,e_,f_},1] :> Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g}, {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]* Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g}, {(d/2)+(e/2)-(1/2)-(g/2), (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/; Factor[f-(a+b+c+g+1)+(d+e)]===0&& Hyp`m`Private`IntegerTest[g], Hyp`m`F[{g_,b_,c_,a_},{d_,e_,f_},1] :> Hyp`m`GAMMA[{(d+e)-(b+c+g),(d+e)-(a+c+g),(d+e)-(a+b+g),d+e-g}, {(d+e)-(c+g),(d+e)-(b+g),(d+e)-(a+g),(d+e)-(a+b+c+g)}]* Hyp`m`F[{d+e-(1+g),(d/2)+(e/2)+(1/2)-(g/2),a,b,c,d-g,e-g}, {(d/2)+(e/2)-(1/2)-(g/2), (d+e)-(a+g),(d+e)-(b+g),(d+e)-(c+g),e,d},1]/; Factor[f-(a+b+c+g+1)+(d+e)]===0&& Hyp`m`Private`IntegerTest[g]}; T7633:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:> Hyp`m`GAMMA[{(a+1)-d,(a+1)-c,(a+1)-b,(a+1)-(b+c+d)}, {(a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),a+1}]* Hyp`m`F[{b,c,d,a+1-(e+f)},{(a+1)-e,(b+c+d)-a,a+1-f},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-1-a]===Factor[c+cc-1-a]===Factor[d+dd-1-a]=== Factor[e+ee-1-a]===Factor[f+ff-1-a]===0&& Hyp`m`Private`IntegerTest[a+1-(e+f)]); T3231:=(Hyp`m`F[{a_,b_,c_},{e_,g_},1]:> Hyp`m`F[{a/2,b/2,c,g-c},{e,g/2,(g+1)/2},1]/; Factor[e-((a/2)+(b/2)+(1/2))]===0&& (Hyp`m`Private`IntegerTest[a/2]||Hyp`m`Private`IntegerTest[b/2]||Hyp`m`Private`IntegerTest[c]|| (Hyp`m`Private`IntegerTest[g-c]&&(Hyp`m`Private`IntegerTest[a]||Hyp`m`Private`IntegerTest[b])))); T3232:=(Hyp`m`F[{a_,d_,e_},{b_,c_},z_]:> (1-Factor[((Factor[1-z])^(1/2)+1)/((Factor[1-z])^(1/2)-1)])^(2*a)* Hyp`m`F[{2*a,1+2*a-b,1+2*a-c},{b,c},Factor[((Factor[1-z])^(1/2)+1)/((Factor[1-z])^(1/2)-1)]]/; Factor[d-(1/2+a)]===Factor[e-(-1-2*a+b+c)]===0); T3233:=(Hyp`m`F[{a_,d_,e_},{b_,c_},z_]:> (1-Factor[((Factor[1-z])^(1/2)-1)/((Factor[1-z])^(1/2)+1)])^(2*a)* Hyp`m`F[{2*a,1+2*a-b,1+2*a-c},{b,c},Factor[((Factor[1-z])^(1/2)-1)/((Factor[1-z])^(1/2)+1)]]/; Factor[d-(1/2+a)]===Factor[e-(-1-2*a+b+c)]===0); T3234:=(Hyp`m`F[{a_,b_,c_},{d_,e_},z_]:> Hyp`m`F[{a/2,b/2},{1/2+a/2+b/2},z]^2/; Factor[c-(a/2+b/2)]===Factor[d-(a+b)]===Factor[e-(1/2+a/2+b/2)]===0); T4306:=(Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1]:> Hyp`m`F[{2*a,2*b,c},{e,c+d},1]/; Factor[e-(a+b+(1/2))]===Factor[f-(c+d)/2]===Factor[g-(c+d+1)/2]===0&& (Hyp`m`Private`IntegerTest[a]||Hyp`m`Private`IntegerTest[b]||Hyp`m`Private`IntegerTest[c]|| (Hyp`m`Private`IntegerTest[d]&&(Hyp`m`Private`IntegerTest[2*a]||Hyp`m`Private`IntegerTest[2*b])))); T2132:=(Hyp`m`F[{a_,b_},{e_},z_]^exp_:1:> Hyp`m`F[{2*a,2*b,a+b}, {2*a+2*b,a+b+(1/2)},z]^(exp/2)/; Factor[e-(a+b+(1/2))]===0); T7634:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:> Hyp`m`GAMMA[{(a+1)-e,(a+1)-f,(2*a+2)-(b+c+d),(2*a+2)-(b+c+d+e+f)}, {a+1,(a+1)-(e+f),(2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)}]* Hyp`m`F[{(2*a+1)-(b+c+d),a+3/2-((b/2)+(c/2)+(d/2)), (a+1)-(c+d),(a+1)-(b+d), (a+1)-(b+c),e,f},{(a+(1/2))-((b/2)+(c/2)+(d/2)), (a+1)-b,(a+1)-c,(a+1)-d, (2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T7635:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:> Hyp`m`GAMMA[{(a+1)-c,(a+1)-d,(a+1)-e,(a+1)-f,(3*a+3)-(2*b+c+d+e+f), (2*a+2)-(b+c+d+e+f)}, {a+1,b,(2*a+2)-(b+d+e+f),(2*a+2)-(b+c+e+f), (2*a+2)-(b+c+d+f),(2*a+2)-(b+c+d+e)}]* Hyp`m`F[{(3*a+2)-(2*b+c+d+e+f),(a*(3/2)+2)- (b+(c/2)+(d/2)+(e/2)+(f/2)),(a+1)-(b+c), (a+1)-(b+d),(a+1)-(b+e),(a+1)-(b+f),(2*a+2)-(b+c+d+e+f)}, {(a*(3/2)+1)-(b+(c/2)+(d/2)+(e/2)+(f/2)),(2*a+2)-(b+d+e+f), (2*a+2)-(b+c+e+f),(2*a+2)-(b+c+d+f),(2*a+2)-(b+c+d+e),(a+1)-b},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T5401:=(Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1]:> Hyp`m`p[{(a+2)-(b+c+d),(a*3+3)-(2*b+2*c+2*d)}, {(2*a+2)-(b+c+d),(2*a+3)-(2*b+2*c+2*d)},-e]* Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)), (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),(a/2),(a/2)+(1/2), (a*3+(3))-(2*b+2*c+2*d+e),e}, {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d, (a*(3/2)+2)-(b+c+d),(a*(3/2)+(3/2))-(b+c+d), (b+c+d+(-1)+e)-a,(2*a+(2))-(b+c+d+e)},1]/; Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0&& Factor[ee-(2*b+2*c+2*d+e+(-2)-2*a)]===0&& Hyp`m`Private`IntegerTest[e]); T9832:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,g_,i_,j_}, {aaaa_,bb_,cc_,dd_,ee_,gg_,ii_,jj_},1]:> Hyp`m`p[{a+1,(2*b+2*c+2*d)-(2*a+1)},{(b+c+d)-a,b+c+d},-j]* Hyp`m`F[{(2*a+1)-(b+c+d),(a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),j}, {(a+1)-b,(a+1)-c,(a+1)-d,(2*a+(2)+j)-(2*b+2*c+2*d)},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[g+gg-(1+a)]=== Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===0&& Factor[e-(a+(1/2)-(b/2)-(c/2)-(d/2))]=== Factor[g-(1/2)-(a+(1/2)-(b/2)-(c/2)-(d/2))]=== Factor[i-(b+c+d-j)]===0&& Hyp`m`Private`IntegerTest[j]); T5402:=(Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1]:> Hyp`m`F[{1+2*a-(b+c+d),(3/2)+a-((b/2)+(c/2)+(d/2)),1+a-(c+d), 1+a-(b+d),1+a-(b+c),(a)/2,(1/2)+(a)/2,e,(3)+a*3-(2*b+2*c+2*d+e)}, {(1/2)+a-((b/2)+(c/2)+(d/2)),1+a-b,1+a-c, 1+a-d,(2)+a*(3/2)-(b+c+d), (3/2)+a*(3/2)-(b+c+d), (2)+2*a-(b+c+d+e),b+c+d+e+(-1)-a},1]* Hyp`m`p[{(2)+2*a-(b+c+d+e),(3)+a*3-(2*b+2*c+2*d)}, {(2)+2*a-(b+c+d),(3)+a*3-(2*b+2*c+2*d+e)},-a]/; Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[ee-2*(b+c+d-1-a)-e]===0&& Hyp`m`Private`IntegerTest[a]); T9833:=(Hyp`m`F[{a_,aa_,b_,c_,d_,f_,h_,e_,j_}, {aaaa_,bb_,cc_,dd_,ff_,hh_,ee_,jj_},1]:> Hyp`m`F[{2*f,((b/2)+(1/2)+f)-((c/2)+(d/2)), ((c/2)+(1/2)+f)-((b/2)+(d/2)), ((d/2)+(1/2)+f)-((b/2)+(c/2)),e}, {((c/2)+(d/2)+(1/2)+f)-(b/2), ((b/2)+(d/2)+(1/2)+f)-(c/2), ((b/2)+(c/2)+(1/2)+f)-(d/2),(e+1+2*f)-(b+c+d)},1]* Hyp`m`p[{(b/2)+(c/2)+(d/2)+(1/2)+f,(b+c+d)-e}, {((b/2)+(c/2)+(d/2)+(1/2)+f)-e,b+c+d},-2*f]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[h+hh-(1+a)]===Factor[j+jj-(1+a)]===0&& Factor[a-((b/2)+(c/2)+(d/2)+h-1)]===0&& Factor[j-(b+c+d-e)]===Factor[f+1/2-h]===0&& Hyp`m`Private`IntegerTest[2*f]); T6531:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_}, {aaaa_,bb_,cc_,dd_,ee_},1]:> (((a*3+1-2*e)-(2*b+2*c+2*d))* Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)), (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),(a/2)+(1/2),(a/2)+1, (a*3+1)-(2*b+2*c+2*d+e),e}, {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d, (a*(3/2)+(3/2))-(b+c+d),(a*(3/2)+1)-(b+c+d),(b+c+d+1+e)-a, (2*a+(2))-(b+c+d+e)},1]* Hyp`m`p[{a-(b+c+d),(a*3+1)-(2*b+2*c+2*d)}, {(2*a+2)-(b+c+d),(2*a+1)-(2*b+2*c+2*d)},-e])/ ((a*3+1)-(2*b+2*c+2*d))/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0&& Factor[ee-(2*b+2*c+2*d+e-(2*a))]===0&& Hyp`m`Private`IntegerTest[e]); T9834:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,g_,i_,j_}, {aaaa_,bb_,cc_,dd_,ee_,gg_,ii_,jj_},1]:> Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)), (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),j},{(a+(1/2))-((b/2)+(c/2)+(d/2)), (a+1)-b,(a+1)-c,(a+1)-d,(2*a+(4)+j)-(2*b+2*c+2*d)},1]* ((b+c+d)-2)/(b+c+d+(-2)-2*j)* Hyp`m`p[{a+1,(2*b+2*c+2*d)-(2*a+3)}, {(b+c+d)-(a+2),(b+c+d)-2},-j]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[g+gg-(1+a)]=== Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]===0&& Factor[e-g+(1/2)]===Factor[(a+1)-((b/2)+(c/2)+(d/2))-e]=== Factor[i-(b+c+d+(-2)-j)]===0&& Hyp`m`Private`IntegerTest[j]); T9831:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_}, {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1] :> Hyp`m`F[{(2*a+1)-(b+c+d),(a+(3/2))-((b/2)+(c/2)+(d/2)), (a+1)-(c+d),(a+1)-(b+d),(a+1)-(b+c),e,f,(a*3+(2))-(b+c+d+e+f+h),h}, {(a+(1/2))-((b/2)+(c/2)+(d/2)),(a+1)-b,(a+1)-c,(a+1)-d, (2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f),(e+f+h)-(a), (2*a+(2))-(b+c+d+h)},1]* Hyp`m`p[{a+1,(a+1)-(e+f),(2*a+2)-(b+c+d+e),(2*a+2)-(b+c+d+f)}, {(a+1)-e,(a+1)-f,(2*a+2)-(b+c+d+e+f),(2*a+2)-(b+c+d)},-h]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]===0&& Factor[g-(a*3+(2))+(b+c+d+e+f+h)]===0&& Hyp`m`Private`IntegerTest[h]); T2191:=(Hyp`m`F[{a_,b_},{c_},z_]:> (1-z)^(-a-b+c)*Hyp`m`F[{-b+c,-a+c},{1-a-b+c},1-z]* Hyp`m`GAMMA[{c,a+b-c},{a,b}]+ Hyp`m`F[{a,b},{1+a+b-c},1-z]*Hyp`m`GAMMA[{c,-a-b+c},{-b+c,-a+c}]); T3261:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:> Hyp`m`GAMMA[{c,c+1-d,1-a,e-(b+c)},{e-b,e-c,c+1-a,1-d}]* Hyp`m`F[{c,d-a,c+1-e},{c+1-a,b+c+1-e},1]- Hyp`m`GAMMA[{d-1,e,b+1-d,c+1-d,1-a,e-(b+c),b+c+1-e}, {1-d,e+1-d,b,c,d-a,d+e-(b+c+1),b+c+2-(d+e)}]* Hyp`m`F[{a+1-d,b+1-d,c+1-d},{2-d,e+1-d},1]); T3262:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:> Hyp`m`GAMMA[{e,e-(b+c)},{e-b,e-c}]*Hyp`m`F[{d-a,b,c},{d,b+c+1-e},1]+ Hyp`m`GAMMA[{d,c,b+c-e,d+e-(a+b+c)},{d-a,b,c,d+e-(b+c)}]* Hyp`m`F[{e-b,e-c,d+e-(a+b+c)},{d+e-(b+c),e+1-(b+c)},1]); T7691:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:> Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f)},{a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f)}]* Hyp`m`F[{a+1-(b+c),d,e,f},{a+1-b,a+1-c,d+e+f-a},1]+ Hyp`m`GAMMA[{a+1-b,a+1-c,a+1-d,a+1-e,a+1-f,2*a+2-(b+c+d+e+f),d+e+f-(a+1)}, {a+1,a+1-(b+c),d,e,f,2*a+2-(b+d+e+f),2*a+2-(c+d+e+f)}]* Hyp`m`F[{a+1-(d+e),a+1-(d+f),a+1-(e+f),2*a+2-(b+c+d+e+f)}, {2*a+2-(b+d+e+f),2*a+2-(c+d+e+f),a+2-(d+e+f)},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T7692:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1]:> Hyp`m`GAMMA[{a+1-d,a+1-e,a+1-f,a+1-(d+e+f),1-c,e+f+1-c,b+e-a,b+f-a}, {a+1,a+1-(d+e),a+1-(d+f),a+1-(e+f),e+1-c,f+1-c,b+e+f-a}]* Hyp`m`F[{e+f-c,1+(e+f-c)/2,a+1-(b+c),a+1-(c+d),e+f-a,e,f}, {(e+f-c)/2,b+e+f-a,d+e+f-a,a+1-c,f+1-c,e+1-c},1]- Hyp`m`GAMMA[{a-b,a+1-c,a+1-d,a+1-e,a+1-f,b+d-a,b+e-a,b+f-a,d+e+f-a,a+1-(d+e+f), 1-c,2*b+1-a}, {a+1,b-a,b+1-c,b+1-d,b+1-e,b+1-f,d,e,f,a+1-(b+c), b+d+e+f-2*a,2*a+1-(b+d+e+f)}]* Hyp`m`F[{2*b-a,1+(2*b-a)/2,b,b+c-a,b+d-a,b+e-a,b+f-a}, {(2*b-a)/2,b+1-a,b+1-c,b+1-d,b+1-e,b+1-f},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T9891:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_}, {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1]:> -Hyp`m`GAMMA[{(2*b+1)-a,a-b,(a+1)-c,(a+1)-d,(a+1)-e,(a+1)-f,(a+1)-g, (b+c+d+e+f+g)-(2*a+1),(b+c)-a,(b+d)-a,(b+e)-a,(b+f)-a,(b+g)-a, (2*a+2)-(c+d+e+f+g)}, {a+1,b-a,c,d,e,f,g,(a*3+2)-(b+c+d+e+f+g),(b+1)-c, (b+1)-d,(b+1)-e,(b+1)-f,(b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)}]* Hyp`m`F[{2*b-a,(b+1)-(a/2),b,(b+c)-a,(b+d)-a, (b+e)-a,(b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)}, {b-(a/2),(b+1)-a,(b+1)-c,(b+1)-d,(b+1)-e,(b+1)-f, (b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)},1]+ Hyp`m`GAMMA[{(2*b+c+d+e)-2*a,(2*a+1)-(b+c+d+e),(a+1)-c,(a+1)-d,(a+1)-e, (a+1)-f,(a+1)-g,(b+c+d+e+f+g)-(2*a+1),(b+c)-a,(b+d)-a,(b+e)-a, (b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)}, {a+1,b-a,f,g,(a*3+2)-(b+c+d+e+f+g),(b+1)-f,(b+1)-g, (2*b+c+d+e+f+g)-(a*3+1),(a+1)-(d+e),(a+1)-(c+e),(a+1)-(c+d), (b+d+e)-a,(b+c+e)-a,(b+c+d)-a}]* Hyp`m`F[{(2*b+c+d+e)-(2*a+1),(b+(c/2)+(d/2)+(e/2)+(1/2))-a, b,(b+c)-a,(b+d)-a, (b+e)-a,(b+c+d+e+f)-(2*a+1),(b+c+d+e+g)-(2*a+1),(a+1)-(f+g)}, {(b+(c/2)+(d/2)+(e/2))-(a+(1/2)),(b+c+d+e)-2*a,(b+d+e)-a, (b+c+e)-a,(b+c+d)-a,(b+1)-f,(b+1)-g,(2*b+c+d+e+f+g)-(a*3+1)},1]\ +Hyp`m`GAMMA[{(2*a+2)-(c+d+e),(b+c+d+e)-(2*a+1),(a+1)-f,(a+1)-g, (b+c+d+e+f+g)-(2*a+1),(b+f)-a,(b+g)-a,(2*a+2)-(c+d+e+f+g)}, {a+1,b-a,(2*a+2)-(c+d+e+f),(2*a+2)-(c+d+e+g), (b+f+g)-a,(b+c+d+e+f)-(2*a+1),(b+c+d+e+g)-(2*a+1),(a+1)-(f+g)}]* Hyp`m`F[{(2*a+1)-(c+d+e),(a+(3/2))-((c/2)+(d/2)+(e/2)), b,(a+1)-(d+e),(a+1)-(c+e),(a+1)-(c+d),f,g,(a*3+2)-(b+c+d+e+f+g)}, {(a+(1/2))-((c/2)+(d/2)+(e/2)),(2*a+2)-(b+c+d+e), (a+1)-c,(a+1)-d,(a+1)-e,(2*a+2)-(c+d+e+f),(2*a+2)-(c+d+e+g), (b+f+g)-a},1]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]===0&& Factor[h-a*3-2+(b+c+d+e+f+g)]===0); T2110:= (Hyp`m`F[{a_,b_},{c_},z_]:> Hyp`m`F[{a/2,1/2+a/2},{1+a-b},(4*z)/(1+z)^2]/(1+z)^a/; Factor[c-1-a+b]===0); T2112:= {(Hyp`m`F[{a_,c_},{b_},z_]:> Hyp`m`F[{2*a,b-1/2},{2*b-1},(2*Sqrt[z])/(-1+Sqrt[z])]/(1-Sqrt[z])^(2*a)/; Factor[c-a-1/2]===0), (Hyp`m`F[{c_,a_},{b_},z_]:> Hyp`m`F[{2*a,b-1/2},{2*b-1},(2*Sqrt[z])/(-1+Sqrt[z])]/(1-Sqrt[z])^(2*a)/; Factor[c-a-1/2]===0)}; T2163:= (Hyp`m`F[{a_,b_},{c_},z_]:>(Hyp`m`F[{b,-a+c},{1-a+b},-(-1+z)^(-1)]* Hyp`m`GAMMA[{a-b,c},{a,-b+c}])/(1-z)^b+ (Hyp`m`F[{a,-b+c},{1+a-b},-(-1+z)^(-1)]* Hyp`m`GAMMA[{-a+b,c},{b,-a+c}])/(1-z)^a); T2133:= (Hyp`m`F[{a_,b_},{c_},z_] :> (1-2*z-2*(z^2-z)^(1/2))^a* Hyp`m`F[{2*a,a+b},{2*a+2*b},2*(z+(z^2-z)^(1/2))]/; Factor[c-(1/2+a+b)]===0); T2134:= (Hyp`m`F[{a_,b_},{c_},z_] :> Hyp`m`F[{a/2,b/2},{1/2+a/2+b/2},4*(1-z)*z]/; Factor[c-(1/2+a/2+b/2)]===0); T2135:= (Hyp`m`F[{a_,b_},{c_},z_] :> Hyp`m`F[{2*a,2*b},{1/2+a+b}, (1-(1-z)^(1/2))/2]/; Factor[c-(1/2+a+b)]===0); T2136:= {(Hyp`m`F[{a_,b_},{c_},z_] :> (2^a*Hyp`m`F[{a/2,1/2+a/2},{1/2+b},z^2/(-2+z)^2])/ (2-z)^a/; Factor[c-2*b]===0), (Hyp`m`F[{b_,a_},{c_},z_] :> (2^a*Hyp`m`F[{a/2,1/2+a/2},{1/2+b},z^2/(-2+z)^2])/ (2-z)^a/; Factor[c-2*b]===0)}; T2137:= {(Hyp`m`F[{a_,b_},{c_},z_] :> Hyp`m`F[{a/2,(-a+2*b)/2},{(1+2*b)/2},z^2/(4*(-1+z))]/(1-z)^(a/2)/; Factor[c-2*b]===0), (Hyp`m`F[{b_,a_},{c_},z_] :> Hyp`m`F[{a/2,(-a+2*b)/2},{(1+2*b)/2},z^2/(4*(-1+z))]/(1-z)^(a/2)/; Factor[c-2*b]===0)}; T3267:= (Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>Hyp`m`F[{a,1+a-e,1+a+b+c-d-e}, {1+a+b-e,1+a+c-e},1]* Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e}, {-a+d,1-e,1+a+b-e,1+a+c-e}]- Hyp`m`F[{1+a-e,1+b-e,1+c-e},{2-e,1+d-e},1]* Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e,-1+e}, {a,b,c,1-e,1+d-e}]); T3268:= (Hyp`m`F[{a_,b_,c_},{d_,e_},1]:>Hyp`m`F[{b,-a+d,-a+e}, {1-a+b,-a-c+d+e},1]* Hyp`m`GAMMA[{a-b,d,e,-a-b-c+d+e}, {a,-b+d,-b+e,-a-c+d+e}]+ Hyp`m`F[{a,-b+d,-b+e},{-b-c+d+e,1+a-b},1]* Hyp`m`GAMMA[{-a+b,d,e,-a-b-c+d+e}, {b,-a+d,-a+e,-b-c+d+e}]); T2192:= (Hyp`m`F[{a_,b_},{c_},z_] :> (Hyp`m`F[{a,1+a-c},{1+a+b-c},(z-1)/z]* Hyp`m`GAMMA[{1+a-c,1+b-c},{1-c,1+a+b-c}])/z^a- z^(1-c)*Hyp`m`F[{1+a-c,1+b-c},{2-c},z]* Hyp`m`GAMMA[{1+a-c,1+b-c,-1+c},{a,b,1-c}]); T3235:= (Hyp`m`F[{a_,b_,n_},{d_,e_},2] :> (Hyp`m`F[{a/2,1/2+a/2,1/2+n/2,n/2}, {1/2+a/2-d/2+n/2,1+a/2-d/2+n/2,1/2+b},1]*Hyp`m`p[-a+d,-n])/ Hyp`m`p[d,-n]/; Factor[e-2*b]===0&& Hyp`m`Private`IntegerTest[n]); T4309:= (Hyp`m`F[{a_,b_,c_,d_},{bb_,cc_,dd_},1]:> Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1/2+a/2, 1+a-c-d,1+a-b-d,1+a-b-c}, {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d, 3/2+(3*a)/2-b-c-d,1+a-b,1+a-c,1+a-d},1]* Hyp`m`GAMMA[{3+2*a-2*b-2*c-2*d,2+2*a-b-c-d}, {3+3*a-2*b-2*c-2*d,2+a-b-c-d}]/; Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0); T4310:= (Hyp`m`F[{a_,b_,c_,d_},{bb_,cc_,dd_},-1]:> Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1+a-c-d, 1+a-b-d,1+a-b-c}, {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d,1+a-b, 1+a-c,1+a-d},-1]* Hyp`m`GAMMA[{2+2*a-b-c-d,1+a/2},{1+a,2+(3*a)/2-b-c-d}]/; Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]===0); T3236:= (Hyp`m`F[{a_,aa_,b_},{aaaa_,bb_},z_]:> (1-z)*(1+z)^(-1-a)*Hyp`m`F[{1/2+a/2,1+a/2},{1+a-b}, (4*z)/(1+z)^2]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===0); T4312:= (Hyp`m`F[{a_,aa_,nn_,n_},{d_,dd_,b_},1]:> Hyp`m`F[{2*a,b-1/2,2*n},{1+2*a-2*d+2*n,2*b-1},2]*Hyp`m`p[{-2*a+2*d},{2*d},-2*n]/; Factor[aa-1/2-a]===Factor[nn-1/2-n]===Factor[dd-1/2-d]===0&& Hyp`m`Private`IntegerTest[2*n]); T4391:= (Hyp`m`F[{a_,c_,d_,e_},{b_,aa_,f_},1] :> Hyp`m`F[{-1/2+b,3/4+b/2,-a+b,c/2,1/2+c/2,d/2,1/2+d/2,e/2, 1/2+e/2},{-1/4+b/2,1/2+a,1/2+b-c/2,b-c/2, 1/2+b-d/2,b-d/2,1/2+b-e/2,b-e/2},1]* Hyp`m`GAMMA[{b,1/2+b,b-c/2-d/2,1/2+b-c/2-d/2,b-c/2-e/2, 1/2+b-c/2-e/2,b-d/2-e/2,1/2+b-d/2-e/2}, {b-c/2,1/2+b-c/2,b-d/2,1/2+b-d/2,b-e/2, 1/2+b-e/2,b-c/2-d/2-e/2,1/2+b-c/2-d/2-e/2}]- Hyp`m`F[{a+2*b-c-d-e,2*b-c-d,2*b-c-e,2*b-d-e}, {3*b-c-d-e,2*a+2*b-c-d-e,1+2*b-c-d-e},1]* Hyp`m`GAMMA[{1/2+a,b,b-c/2-d/2,1/2+b-c/2-d/2, a+2*b-c-d-e,b-c/2-e/2,1/2+b-c/2-e/2, b-d/2-e/2,1/2+b-d/2-e/2,-b+c/2+d/2+e/2, 1/2-b+c/2+d/2+e/2}, {c/2,1/2+c/2,d/2,1/2+d/2,3*b-c-d-e,b-c/2-d/2-e/2, 1/2+b-c/2-d/2-e/2,a+b-c/2-d/2-e/2, 1/2+a+b-c/2-d/2-e/2,e/2,1/2+e/2}]/; Factor[aa-2*a]===Factor[f-(1-2*b+c+d+e)]===0); T5468:= (Hyp`m`F[{a_,b_,c_,d_,e_},{bb_,cc_,dd_,ee_},1] :> -Hyp`m`F[{3+2*a-2*b-2*c-2*d,3+3*a-2*b-2*c-2*d-e, 3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e, 3+2*a-2*b-2*c-d-e}, {4+2*a-2*b-2*c-2*d-e,4+3*a-3*b-2*c-2*d-e, 4+3*a-2*b-3*c-2*d-e,4+3*a-2*b-2*c-3*d-e},1]* Hyp`m`GAMMA[{1+a-b,1+a-c,3+2*a-2*b-2*c-2*d, 1+a-d,3+3*a-2*b-2*c-2*d-e,3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e, 3+2*a-2*b-2*c-d-e,-3-2*a+2*b+2*c+2*d+e}, {a,b,c,d,4+3*a-2*b-2*c-3*d-e,4+3*a-2*b-3*c-2*d-e,4+3*a-3*b-2*c-2*d-e, 3+2*a-2*b-2*c-2*d-e,e}] + Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,a/2,1/2+a/2, 1+a-c-d,1+a-b-d,1+a-b-c,e, 3+3*a-2*b-2*c-2*d-e}, {1/2+a-b/2-c/2-d/2,2+(3*a)/2-b-c-d, 3/2+(3*a)/2-b-c-d,1+a-b,1+a-c,1+a-d, 2+2*a-b-c-d-e,-1-a+b+c+d+e},1]* Hyp`m`GAMMA[{3+2*a-2*b-2*c-2*d,2+2*a-b-c-d, 3+3*a-2*b-2*c-2*d-e,2+a-b-c-d-e}, {3+3*a-2*b-2*c-2*d,2+a-b-c-d, 3+2*a-2*b-2*c-2*d-e,2+2*a-b-c-d-e}]+ Hyp`m`F[{5+4*a-3*b-3*c-3*d-2*e, 7/2+2*a-(3*b)/2-(3*c)/2-(3*d)/2-e, 2+(3*a)/2-b-c-d-e,5/2+(3*a)/2-b-c-d-e, 2+a-b-c-d,3+3*a-2*b-2*c-2*d-e, 3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e, 3+2*a-2*b-2*c-d-e}, {5/2+2*a-(3*b)/2-(3*c)/2-(3*d)/2-e, 4+(5*a)/2-2*b-2*c-2*d-e, 7/2+(5*a)/2-2*b-2*c-2*d-e,4+3*a-2*b-2*c-2*d-2*e, 3+a-b-c-d-e,3+2*a-2*b-c-d-e, 3+2*a-b-2*c-d-e,3+2*a-b-c-2*d-e},1]* Hyp`m`GAMMA[{1+a-b,1+a-c,3+2*a-2*b-2*c-2*d,1+a-d, 6+4*a-3*b-3*c-3*d-2*e,3+3*a-2*b-2*c-2*d-e, 3+2*a-b-2*c-2*d-e,3+2*a-2*b-c-2*d-e, 3+2*a-2*b-2*c-d-e,-2-a+b+c+d+e}, {a,1+a-b-c,1+a-b-d,1+a-c-d, 7+5*a-4*b-4*c-4*d-2*e,3+2*a-2*b-2*c-2*d-e, 3+2*a-b-c-2*d-e,3+2*a-b-2*c-d-e, 3+2*a-2*b-c-d-e,e}]/; Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[ee-(-2-2*a+2*b+2*c+2*d+e)]===0); T6501:= (Hyp`m`F[{a_,aa_,b_,c_,d_,n_},{aaaa_,bb_,cc_,dd_,nn_},1]:> Hyp`m`F[{1+2*a-b-c-d,3/2+a-b/2-c/2-d/2,1+a-c-d, 1+a-b-d,1+a-b-c,1+a/2,1/2+a/2, 2+3*a-2*b-2*c-2*d-n,n}, {1/2+a-b/2-c/2-d/2,1+a-b,1+a-c,1+a-d, 1+(3*a)/2-b-c-d,3/2+(3*a)/2-b-c-d, -a+b+c+d+n,2+2*a-b-c-d-n},1]* Hyp`m`p[{2+3*a-2*b-2*c-2*d,1+a-b-c-d}, {2+2*a-2*b-2*c-2*d,2+2*a-b-c-d},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[nn-(-1-2*a+2*b+2*c+2*d+n)]===0&& Hyp`m`Private`IntegerTest[n]); T6532:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_}, {aaaa_,bb_,cc_,dd_,ee_},-1]:> Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d}, {1+a-c,1+a-d,-a+2*b+c+d},-1]* Hyp`m`GAMMA[{1+2*b,1+a-b},{1+b,1+a}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[e-(1+2*a-2*b-c-d)]===0); T7636:= (Hyp`m`F[{a_,aa_,b_,c_,e_,d_,f_}, {aaaa_,bb_,cc_,ee_,dd_,ff_},1]:> Hyp`m`F[{2*c,b,1/2+a-2*d},{1+2*a-b-2*d,1/2+a},1]* Hyp`m`GAMMA[{1+2*a-2*b,1+2*a-2*c,1+2*a-2*d, 1+2*a-b-2*c-2*d},{1+2*a,1+2*a-2*b-2*c, 1+2*a-b-2*d,1+2*a-2*c-2*d}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[e-1/2-c]===Factor[f-1/2-d]===0); T7693:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_}, {aaaa_,bb_,cc_,dd_,ee_,ff_},1] :> -(Hyp`m`F[{-a+2*b,1-a/2+b,b,-a+b+c,-a+b+d,-a+b+e, -a+b+f},{-a/2+b,1-a+b,1+b-c,1+b-d, 1+b-e,1+b-f},1]* Hyp`m`GAMMA[{a-b,1-a+2*b,-b+c,-a+b+c,1-d,1+a-d, 1-e,1+a-e,1-f,1+a-f}, {1+a,-a+b,-a+c,c,1+a-b-d,1+b-d,1+a-b-e, 1+b-e,1+a-b-f,1+b-f}])- Hyp`m`F[{-a+2*c,1-a/2+c,c,-a+b+c,-a+c+d,-a+c+e, -a+c+f},{-a/2+c,1-a+c,1-b+c,1+c-d,1+c-e, 1+c-f},1]*Hyp`m`GAMMA[{a-c,b-c,-a+b+c,1-a+2*c,1-d, 1+a-d,1-e,1+a-e,1-f,1+a-f}, {1+a,-a+b,b,-a+c,1+a-c-d,1+c-d,1+a-c-e, 1+c-e,1+a-c-f,1+c-f}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T7637:= (Hyp`m`F[{a_,aa_,b_,e_,c_,d_,f_}, {aaaa_,bb_,ee_,cc_,dd_,ff_},1] :> Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d}, {1+a-c,1+a-d,-a+2*b+c+d},1]* Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b},{1+a,1+2*a-4*b}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[e-1/2-b]===Factor[f-(1+2*a-2*b-c-d)]===0); T9835:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,n_}, {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,nn_},1] :> Hyp`m`F[{-b+e+n,1-b/2+e/2+n/2,e,1+a-b-c, 1+a-b-d,1+a-b-f,-1-2*a+c+d+e+f+n, -a+e+n,n},{-b/2+e/2+n/2,1-b+n,-a+c+e+n, -a+d+e+n,-a+e+f+n,2+2*a-b-c-d-f,1+a-b, 1-b+e},1]*Hyp`m`p[{1+a,b,1+a-c-e,1+a-d-e, 1+a-e-f,-1-2*a+b+c+d+f+n}, {1+a-c,1+a-d,1+a-e,b-e,1+a-f, -1-2*a+b+c+d+e+f+n},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[g+gg-(1+a)]===Factor[n+nn-(1+a)]=== Factor[g-(2+3*a-b-c-d-e-f-n)]===0&& Hyp`m`Private`IntegerTest[n]); T9836:= (Hyp`m`F[{a_,aa_,b_,c_,d_,A_,B_,C_,n_}, {aaaa_,bb_,cc_,dd_,AA_,BB_,CC_,nn_},1]:> Hyp`m`F[{-A/2-B/2-C/2+(3*n)/2,1-A/4-B/4-C/4+(3*n)/4, -A/2-B/2+C/2+n/2,A/2-B/2-C/2+n/2, -A/2+B/2-C/2+n/2,-a+c+n,-b-c+n,-a+b+n,n}, {-A/4-B/4-C/4+(3*n)/4,1-C+n,1-A+n,1-B+n, -c+n,-a+b+c+n,-b+n,-a+n},1]* Hyp`m`p[{1+c,1-C+n,1-A+n,1-B+n,1+a,1+b, 1+a-b-c},{1+b+c,1-A/2-B/2-C/2+(3*n)/2, 1-A/2-B/2+C/2+n/2,1-A/2+B/2-C/2+n/2, 1+A/2-B/2-C/2+n/2,1+a-b,1+a-c},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[d-(a-b-c)]=== Factor[B+BB-(A+B+C+n)/2]===Factor[C+CC-(A+B+C+n)/2]===Factor[n+nn-(A+B+C+n)/2]===0&& Hyp`m`Private`IntegerTest[n]); T8731:= (Hyp`m`F[{a_,aa_,c_,d_,e_,b_,f_,n_}, {aaaa_,cc_,dd_,ee_,bb_,ff_,nn_},-1]:> Hyp`m`F[{a/2+n/2,1+a/4+n/4,n,c/2,1/2+c/2,d/2,1/2+d/2,e/2, 1/2+e/2,1/2+a-c/2-d/2-e/2+n/2, 1+a-c/2-d/2-e/2+n/2}, {a/4+n/4,1+a/2-n/2,1+a/2-c/2+n/2,1/2+a/2-c/2+n/2, 1+a/2-d/2+n/2,1/2+a/2-d/2+n/2,1+a/2-e/2+n/2, 1/2+a/2-e/2+n/2,1/2-a/2+c/2+d/2+e/2, -a/2+c/2+d/2+e/2},1]* Hyp`m`p[{1+a-c+n,1+a-d+n,1+a-e+n,1+a-c-d-e+n}, {1+a+n,1+a-c-d+n,1+a-c-e+n,1+a-d-e+n},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[n+nn-(1+a)]=== Factor[b-(1/2+a/2-n/2)]===Factor[f-(1+2*a-c-d-e+n)]===0&& Hyp`m`Private`IntegerTest[n]); T8732:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,n_}, {aaaa_,bb_,cc_,dd_,ee_,ff_,nn_},-1]:> Hyp`m`F[{a/2+e/2,1+a/4+e/4,e,c/2,1/2+c/2,d/2,1/2+d/2, 1/2+a-c/2-d/2+e/2-n/2,1+a-c/2-d/2+e/2-n/2, 1/2+n/2,n/2},{a/4+e/4,1+a/2-e/2,1+a/2-c/2+e/2, 1/2+a/2-c/2+e/2,1+a/2-d/2+e/2,1/2+a/2-d/2+e/2, 1/2-a/2+c/2+d/2+n/2,-a/2+c/2+d/2+n/2, 1/2+a/2+e/2-n/2,1+a/2+e/2-n/2},1]* Hyp`m`p[{1+a-c+e,1+a-d+e,1+a,1+a-c-d}, {1+a+e,1+a-c-d+e,1+a-c,1+a-d},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]=== Factor[n+nn-(1+a)]=== Factor[b-(1/2+a/2-e/2)]===Factor[f-(1+2*a-c-d+e-n)]===0&& Hyp`m`Private`IntegerTest[n]); T9892:= (Hyp`m`F[{a_,aa_,b_,c_,f_,d_,g_,e_,h_}, {aaaa_,bb_,cc_,ff_,dd_,gg_,ee_,hh_},1]:> Hyp`m`F[{1/2+a-b,2*c,2*d,2*e}, {1/2+a,1+2*a-2*b,-2*a+2*c+2*d+2*e},1]* Hyp`m`GAMMA[{1/2+a-c,1+a-c,1/2+a-d,1+a-d,1/2+a-e, 1+a-e,1/2+a-c-d-e,1+a-c-d-e}, {1/2+a,1+a,1/2+a-c-d,1+a-c-d,1/2+a-c-e, 1+a-c-e,1/2+a-d-e,1+a-d-e}]+ Hyp`m`F[{3/2+3*a-b-2*c-2*d-2*e,1+2*a-2*c-2*d, 1+2*a-2*c-2*e,1+2*a-2*d-2*e}, {3/2+3*a-2*c-2*d-2*e,2+4*a-2*b-2*c-2*d-2*e, 2+2*a-2*c-2*d-2*e},1]* Hyp`m`GAMMA[{1+a-b,1/2+a-c,1+a-c,1/2+a-d,1+a-d, 3/2+3*a-b-2*c-2*d-2*e,1/2+a-e,1+a-e, -1/2-a+c+d+e,-a+c+d+e}, {1+a,c,1/2+c,d,1/2+d,3/2+3*a-2*c-2*d-2*e, 1+2*a-b-c-d-e,3/2+2*a-b-c-d-e,e,1/2+e}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]=== Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-1/2-e]===0); T9893:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_,g_,h_}, {aaaa_,bb_,cc_,dd_,ee_,ff_,gg_,hh_},1] :> -Hyp`m`F[{-a+2*b,1-a/2+b,b,-a+b+c,-a+b+d,-a+b+e, -a+b+f,-a+b+g,2+2*a-c-d-e-f-g}, {-a/2+b,1-a+b,1+b-c,1+b-d,1+b-e,1+b-f, 1+b-g,-1-3*a+2*b+c+d+e+f+g},1]* Hyp`m`GAMMA[{a-b,1-a+2*b,1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e,-a+b+e, 1+a-f,-a+b+f,1+a-g,2+2*a-c-d-e-f-g,-a+b+g,-1-2*a+b+c+d+e+f+g}, {1+a,-a+b,1+b-c,c,1+b-d,d,1+b-e,e,1+b-f,f,1+b-g,2+3*a-b-c-d-e-f-g,g, -1-3*a+2*b+c+d+e+f+g}] + Hyp`m`F[{2+3*a-c-d-e-f-2*g, 2+(3*a)/2-c/2-d/2-e/2-f/2-g,b,1+a-c-g, 1+a-d-g,1+a-e-g,1+a-f-g, 2+2*a-c-d-e-f-g,2+3*a-b-c-d-e-f-g}, {1+(3*a)/2-c/2-d/2-e/2-f/2-g, 3+3*a-b-c-d-e-f-2*g,2+2*a-d-e-f-g, 2+2*a-c-e-f-g,2+2*a-c-d-f-g, 2+2*a-c-d-e-g,1+a-g,1+b-g},1]* Hyp`m`GAMMA[{1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e, -a+b+e,1+a-f,-a+b+f,3+3*a-c-d-e-f-2*g, 2+2*a-c-d-e-f-g,-1-2*a+b+c+d+e+f+g, -2-3*a+b+c+d+e+f+2*g}, {1+a,-a+b,1+b-g,2+2*a-c-d-e-g, 2+2*a-c-d-f-g,2+2*a-c-e-f-g, 2+2*a-d-e-f-g,g,-1-2*a+b+c+d+e+g, -1-2*a+b+c+d+f+g,-1-2*a+b+c+e+f+g, -1-2*a+b+d+e+f+g}]+ Hyp`m`F[{-2-3*a+2*b+c+d+e+f+2*g, (-3*a)/2+b+c/2+d/2+e/2+f/2+g,b, -1-2*a+b+d+e+f+g,-1-2*a+b+c+e+f+g, -1-2*a+b+c+d+f+g,-1-2*a+b+c+d+e+g, -a+b+g,g},{-1-(3*a)/2+b+c/2+d/2+e/2+f/2+g, -1-3*a+b+c+d+e+f+2*g,-a+b+c+g,-a+b+d+g, -a+b+e+g,-a+b+f+g,-1-2*a+b+c+d+e+f+g, -1-3*a+2*b+c+d+e+f+g},1]* Hyp`m`GAMMA[{1+a-c,-a+b+c,1+a-d,-a+b+d,1+a-e, -a+b+e,1+a-f,-a+b+f,2+3*a-b-c-d-e-f-2*g, 1+a-g,-a+b+g,-1-3*a+2*b+c+d+e+f+2*g}, {1+a,-a+b,1+a-c-g,1+a-d-g,1+a-e-g, 1+a-f-g,2+3*a-b-c-d-e-f-g,-a+b+c+g, -a+b+d+g,-a+b+e+g,-a+b+f+g, -1-3*a+2*b+c+d+e+f+g}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]===Factor[h-(2+3*a-b-c-d-e-f-g)]===0); T9837:= (Hyp`m`F[{a_,aa_,c_,d_,e_,b_,f_,g_,n_}, {aaaa_,cc_,dd_,ee_,bb_,ff_,gg_,nn_},1]:> Hyp`m`F[{-2+2*b,b,-2-a+2*b+c,-2-a+2*b+d,1+a-c-d,n}, {-1+b,1+a-c,1+a-d,-2-a+2*b+c+d, -3-2*a+4*b+n},1]*Hyp`m`p[{1+a,4+2*a-4*b}, {2+a-2*b,2+2*a-2*b},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[n+nn-(1+a)]=== Factor[e-(3+2*a-2*b-c-d)]===Factor[f+1/2-b]===Factor[g-(2+2*a-2*b-n)]===0&& Hyp`m`Private`IntegerTest[n]); T111031:= (Hyp`m`F[{a_,aa_,c_,f_,d_,g_,e_,h_,i_,j_,n_}, {aaaa_,cc_,ff_,dd_,gg_,ee_,hh_,ii_,jj_,nn_},1]:> Hyp`m`F[{2*a-n,1+a-n/2,2*c,2*d,2*e,1/2+a-n, 1+4*a-2*c-2*d-2*e-n,n}, {a-n/2,1+2*a-2*c-n,1+2*a-2*d-n,1+2*a-2*e-n, 1/2+a,-2*a+2*c+2*d+2*e,1+2*a-2*n},-1]* Hyp`m`p[{1+2*a,1+2*a-2*c-2*d,1+2*a-2*c-2*e, 1+2*a-2*d-2*e},{1+2*a-2*c,1+2*a-2*d,1+2*a-2*e, 1+2*a-2*c-2*d-2*e},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[n+nn-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]===Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]=== Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-1/2-e]=== Factor[i-(1/2+2*a-c-d-e-n/2)]===Factor[j-(1+2*a-c-d-e-n/2)]===0&& Hyp`m`Private`IntegerTest[n]); T111032:= (Hyp`m`F[{a_,aa_,e_,c_,f_,d_,g_,h_,i_,j_,n_}, {aaaa_,ee_,cc_,ff_,dd_,gg_,hh_,ii_,jj_,nn_},1]:> Hyp`m`F[{2*a-e,1+a-e/2,1/2+a-e,2*c,2*d,e, 1+4*a-2*c-2*d-e-2*n,2*n}, {a-e/2,1/2+a,1+2*a-2*c-e,1+2*a-2*d-e,1+2*a-2*e, -2*a+2*c+2*d+2*n,1+2*a-e-2*n},-1]* Hyp`m`p[{1+2*a,1+2*a-2*c-2*d,1+2*a-2*c-e,1+2*a-2*d-e}, {1+2*a-2*c,1+2*a-2*d,1+2*a-e,1+2*a-2*c-2*d-e},-2*n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[n+nn-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]===Factor[i+ii-(1+a)]===Factor[j+jj-(1+a)]=== Factor[f-1/2-c]===Factor[g-1/2-d]===Factor[h-(1/2+2*a-c-d-e/2-n)]=== Factor[i-(1+2*a-c-d-e/2-n)]===Factor[j-1/2-n]===0&& Hyp`m`Private`IntegerTest[2*n]); T9894:= (Hyp`m`F[{a_,aa_,b_,f_,c_,d_,g_,e_,h_}, {aaaa_,bb_,ff_,cc_,dd_,gg_,ee_,hh_},1] :> (-Hyp`m`F[{2+3*a-4*b-2*e,2+(3*a)/2-2*b-e,1+a-b-e, 3/2+a-b-e,1+a-2*b,1+2*a-2*b-e, 1+a-2*b+c-e,1+a-2*b+d-e, 2+3*a-4*b-c-d-e}, {1+(3*a)/2-2*b-e,2+2*a-3*b-e,3/2+2*a-3*b-e, 2+2*a-2*b-2*e,2+a-2*b-e,2+2*a-2*b-c-e, 2+2*a-2*b-d-e,1+c+d-e},1]* Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-c,1+a-d,-a+2*b+c+d,3+3*a-4*b-2*e, 1+a-e,1+a-2*b+c-e,2+3*a-4*b-c-d-e,1+a-2*b+d-e,-1-a+2*b+e}, {1+a,2*b,c,1+2*a-2*b-c-d,d,3+4*a-6*b-2*e,1+a-2*b-e,2+2*a-2*b-c-e, 2+2*a-2*b-d-e,1+c+d-e,e}]) + Hyp`m`F[{2*b,-a+2*b+c,-a+2*b+d,1+a-c-d,e}, {1+a-c,1+a-d,-a+2*b+c+d,-2*a+4*b+e},1]* Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-e,1+2*a-4*b-e}, {1+a,1+2*a-4*b,1+a-2*b-e,1+2*a-2*b-e}]+ Hyp`m`F[{1+2*a-4*b,1+2*a-2*b-e,1+a-2*b+c-e, 1+a-2*b+d-e,2+3*a-4*b-c-d-e}, {2+2*a-4*b-e,2+3*a-4*b-c-e,2+3*a-4*b-d-e, 1+a-2*b+c+d-e},1]* Hyp`m`GAMMA[{1+a-2*b,1+2*a-2*b,1+a-c,1+a-d, -a+2*b+c+d,1+a-e,1+a-2*b+c-e, 2+3*a-4*b-c-d-e,1+a-2*b+d-e,-1-2*a+4*b+e}, {1+a,2*b,-a+2*b+c,1+a-c-d,-a+2*b+d,1+a-2*b-e, 2+3*a-4*b-c-e,2+3*a-4*b-d-e,1+a-2*b+c+d-e, e}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===Factor[g+gg-(1+a)]=== Factor[h+hh-(1+a)]=== Factor[f-1/2-b]===Factor[g-(1+2*a-2*b-c-d)]===Factor[h-(1+2*a-2*b-e)]===0); T5403:= (Hyp`m`F[{x_,y_,a_,c_,n_},{d_,b_,e_,f_},1] :> Hyp`m`F[{-2*a+2*b,x,y,n},{2*b-x,2*b-y,2*b-n},1]* Hyp`m`p[{2*b-x,2*b-y},{2*b,2*b-x-y},-n]/; Factor[c-1/2-a]===Factor[d-2*a]===Factor[e-1/2-b]=== Factor[f-(1-2*b+n+x+y)]===0&& Hyp`m`Private`IntegerTest[n]); T6533:= (Hyp`m`F[{a_,aa_,b_,x_,y_,n_},{aaaa_,bb_,xx_,yy_,nn_},-1]:> Hyp`m`F[{n,x,y},{-a+n+x+y,1+a-b},1]* Hyp`m`p[{1+a,1+a-x-y},{1+a-x,1+a-y},-n]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[x+xx-(1+a)]===Factor[y+yy-(1+a)]=== Factor[n+nn-(1+a)]===0&& Hyp`m`Private`IntegerTest[n]); T6534:=(Hyp`m`F[{a_,aa_,b_,c_,d_,e_},{aaaa_,bb_,cc_,dd_,ee_},-1]:> Hyp`m`F[{1+a-b-c,d,e},{1+a-b,1+a-c},1]* Hyp`m`GAMMA[{1+a-d,1+a-e},{1+a,1+a-d-e}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===0); T3217:=(Hyp`m`F[{a_,b_,c_},{d_,e_},1]:> Hyp`m`F[{-1-a+d+e,1/2-a/2+d/2+e/2,-a+e,-a+d,b,c}, {-1/2-a/2+d/2+e/2,d,e,-a-b+d+e,-a-c+d+e},-1]* Hyp`m`GAMMA[{-a+d+e,-a-b-c+d+e},{-a-b+d+e,-a-c+d+e}]); T3263:= (Hyp`m`F[{a_,b_,c_},{d_,e_},1] :> Hyp`m`F[{1+a-d,-c+e,a}, {1+a+b-d,1+a-c},1]* Hyp`m`GAMMA[{1-c,d,-a-b+d,1+a-e}, {1+a-c,-a+d,-b+d,1-e}]+ Hyp`m`F[{1-b,-a-b-c+d+e,-b+d},{1-a-b+d,1-b-c+d},1]* Hyp`m`GAMMA[{1-c,a+b-d,d,1+a-e,e,-a-b-c+d+e}, {a,b,1-b-c+d,1+a+b-d-e,-c+e,-a-b+d+e}]); T3264:= (Hyp`m`F[{a_,b_,c_},{d_,e_},1] :> Hyp`m`F[{-a+d,b,c},{d,1+b+c-e},1]* Hyp`m`GAMMA[{1+b-e,1+c-e},{1-e,1+b+c-e}]- Hyp`m`F[{1+c-e,1+b-e,1+a-e},{1+d-e,2-e},1]* Hyp`m`GAMMA[{d,1+a-e,1+b-e,1+c-e,-1+e}, {a,b,c,1-e,1+d-e}]); T4362:= (Hyp`m`F[{a_,b_,c_,d_},{e_,f_,g_},1] :> Hyp`m`F[{-1-a+e+f,1/2-a/2+e/2+f/2,-a+f,-a+e,b,c,d}, {-1/2-a/2+e/2+f/2,e,f,-a-b+e+f,-a-c+e+f, -a-d+e+f},1]*Hyp`m`GAMMA[{-a+e+f,-a-b-c+e+f, -a-b-d+e+f,-a-c-d+e+f}, {-a-b+e+f,-a-c+e+f,-a-d+e+f,-a-b-c-d+e+f}] -Hyp`m`F[{-a-b-c+e+f,-a-b-d+e+f,-a-c-d+e+f, -b-c-d+e+f},{-a-b-c-d+2*e+f, -a-b-c-d+e+2*f,1-a-b-c-d+e+f},1]* Hyp`m`GAMMA[{e,a+b+c+d-e-f,f,-a-b-c+e+f, -a-b-d+e+f,-a-c-d+e+f,-b-c-d+e+f}, {a,b,c,d,-a-b-c-d+e+f,-a-b-c-d+2*e+f, -a-b-c-d+e+2*f}]/; Factor[g-(1+a+b+c+d-e-f)]===0); T7694:= (Hyp`m`F[{a_,aa_,b_,c_,d_,e_,f_},{aaaa_,bb_,cc_,dd_,ee_,ff_},1] :> Hyp`m`F[{-d+e+f,1-d/2+e/2+f/2,1+a-b-d,-a+e+f, 1+a-c-d,e,f},{-d/2+e/2+f/2,-a+b+e+f,1+a-d, -a+c+e+f,1-d+f,1-d+e},1]* Hyp`m`GAMMA[{1+a-b,1-d,1+a-e,-a+c+e,1+a-f, 1+a-b-e-f,-a+c+f,1-d+e+f}, {1+a,-a+c,1+a-b-e,1-d+e,1+a-b-f,1+a-e-f, 1-d+f,-a+c+e+f}]+ Hyp`m`F[{2+2*a-2*b-d-e-f,2+a-b-d/2-e/2-f/2,1+a-b-d, 1-b,2+2*a-b-c-d-e-f,1+a-b-f,1+a-b-e}, {1+a-b-d/2-e/2-f/2,2+a-b-e-f, 2+2*a-b-d-e-f,1-b+c,2+a-b-d-e, 2+a-b-d-f},1]*Hyp`m`GAMMA[{1+a-b,1+a-c,1-d,1+a-d, 1+a-e,-a+c+e,1+a-f,3+2*a-2*b-d-e-f, 2+2*a-b-c-d-e-f,-a+c+f,-1-a+b+e+f}, {1+a,b,1-b+c,1+a-c-d,2+a-b-d-e,e, 2+a-b-d-f,2+2*a-b-c-e-f,2+2*a-b-d-e-f,f, -1-2*a+b+c+e+f}]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===Factor[d+dd-(1+a)]=== Factor[e+ee-(1+a)]===Factor[f+ff-(1+a)]===0); T2138:= (Hyp`m`F[{a_,b_},{c_},z_] :> (1-z)^(-1+c)* Hyp`m`F[{(-a+c)/2,(-1+a+c)/2},{c},4*(1-z)*z]/; Factor[b-1+a]===0); T2139:= (Hyp`m`F[{c_,b_},{a_},z_] :> (1/2)^(1-a)*(1+(1-z)^(1/2))^(1-a)* Hyp`m`F[{a-2*c,1-a+2*c},{a},(1-(1-z)^(1/2))/2]/; Factor[b+1/2-a+c]===0); T4331:= (Hyp`m`F[{a_,aa_,b_,c_},{aaaa_,bb_,cc_},z_] :> (1-z)^(-1-a)*(1+z)*Hyp`m`F[{1/2+a/2,1+a/2,1+a-b-c}, {1+a-b,1+a-c},(-4*z)/(-1+z)^2]/; Factor[aa-1-aaaa]===Factor[(a/2)-aaaa]=== Factor[b+bb-(1+a)]===Factor[c+cc-(1+a)]===0); T3238:= (Hyp`m`F[{a_,d_,e_},{b_,c_},z_] :> -((2^(2*a-1)*(1+(1-z)^(1/2))^(2*a-1)* Hyp`m`F[{2*a-1,1/2+a,1/2+a-b,2*a-c},{a-1/2,b,c}, (-2-2*(1-z)^(1/2)+z)/z])/((1-z)^(1/2)*z^(2*a-1)))/; Factor[d-1/2-a]===Factor[e-(-2*a+b+c)]===0); T2140:= {(Hyp`m`F[{a_,aa_},{b_},z_] :> (2^(2*a)*(1+(1-z)^(1/2))^(2*a)* Hyp`m`F[{2*a,1+2*a-b},{b},(1+(1-z)^(1/2))^2/z])/z^(2*a)/; Factor[aa-a-1/2]===0), (Hyp`m`F[{aa_,a_},{b_},z_] :> (2^(2*a)*(1+(1-z)^(1/2))^(2*a)* Hyp`m`F[{2*a,1+2*a-b},{b},(1+(1-z)^(1/2))^2/z])/z^(2*a)/; Factor[aa-a-1/2]===0)}; T2141:= {(Hyp`m`F[{a_,aa_},{b_},z_] :> -(2^(2*a)*(1+(1-z)^(1/2))^(2*a)*z^(1-2*a)* Hyp`m`F[{-1+2*a,1/2+a,2*a-b},{-1/2+a,b},(1+(1-z)^(1/2))^2/z]) /(2*(1+(1-z)^(1/2)-z))/; Factor[aa-a-1/2]===0), (Hyp`m`F[{aa_,a_},{b_},z] :> -(2^(2*a)*(1+(1-z)^(1/2))^(2*a)*z^(1-2*a)* Hyp`m`F[{-1+2*a,1/2+a,2*a-b},{-1/2+a,b},(1+(1-z)^(1/2))^2/z]) /(2*(1+(1-z)^(1/2)-z))/; Factor[aa-a-1/2]===0)}; T4332:= (Hyp`m`F[{b_,x_,y_,n_},{xx_,yy_,nn_},1] :> Hyp`m`F[{x,y,(x+xx)/2-b/2,1/2+(x+xx)/2-b/2,n}, {(x+xx)-b,(x+xx)/2,1/2+(x+xx)/2,1-(xx)+n+y},1]* Hyp`m`p[{(x+xx),(xx)-y},{(xx),(x+xx)-y},-n]/; Factor[yy+y-xx-x]===Factor[n+nn-xx-x]===0&&Hyp`m`Private`IntegerTest[n]); T3237:= {(Hyp`m`F[{x_,y_,n_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2, 1-a-b+n+x+y,x,y,n}, {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y}, -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/; Hyp`m`Private`IntegerTest[n]), (Hyp`m`F[{x_,n_,y_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2, 1-a-b+n+x+y,x,y,n}, {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y}, -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/; Hyp`m`Private`IntegerTest[n]), (Hyp`m`F[{n_,y_,x_},{b_,a_},1] :> Hyp`m`F[{-a+n+x+y,1-a/2+n/2+x/2+y/2, 1-a-b+n+x+y,x,y,n}, {-a/2+n/2+x/2+y/2,b,1-a+n+y,1-a+n+x,1-a+x+y}, -1]*Hyp`m`p[{a-x,a-y},{a,a-x-y},-n]/; Hyp`m`Private`IntegerTest[n])}; T3240:= (Hyp`m`F[{c_,b_,d_},{a_,e_},1] :> Hyp`m`F[{-1/2+a,3/4+a/2,b,c/2,1/2+c/2,a/2-d/2,1/2+a/2-d/2}, {-1/4+a/2,1/2+a-b,1/2+a-c/2,a-c/2,1/2+a/2+d/2, a/2+d/2},1]*Hyp`m`GAMMA[{2*a,2*a-2*b-c,a-b+d,a-c+d}, {2*a-2*b,2*a-c,a+d,a-b-c+d}]/; Factor[e-(a-b+d)]===0); Regel[Global`rs01]:=Transfor`m`Trs01; Regel[2103]:=Transfor`m`T2103; Regel[2104]:=Transfor`m`T2104; Regel[2106]:=Transfor`m`T2106; Regel[2107]:=Transfor`m`T2107; Regel[2131]:=Transfor`m`T2131; Regel[2132]:=Transfor`m`T2132; Regel[3204]:=Transfor`m`T3204; Regel[3205]:=Transfor`m`T3205; Regel[3206]:=Transfor`m`T3206; Regel[3207]:=Transfor`m`T3207; Regel[3217]:=Transfor`m`T3217; Regel[3239]:=Transfor`m`T3239; Regel[4301]:=Transfor`m`T4301; Regel[4302]:=Transfor`m`T4302; Regel[7631]:=Transfor`m`T7631; Regel[7632]:=Transfor`m`T7632; Regel[4303]:=Transfor`m`T4303; Regel[4304]:=Transfor`m`T4304; Regel[7633]:=Transfor`m`T7633; Regel[3231]:=Transfor`m`T3231; Regel[3232]:=Transfor`m`T3232; Regel[3233]:=Transfor`m`T3233; Regel[3234]:=Transfor`m`T3234; Regel[4306]:=Transfor`m`T4306; Regel[7634]:=Transfor`m`T7634; Regel[7635]:=Transfor`m`T7635; Regel[5401]:=Transfor`m`T5401; Regel[9832]:=Transfor`m`T9832; Regel[5402]:=Transfor`m`T5402; Regel[9833]:=Transfor`m`T9833; Regel[6531]:=Transfor`m`T6531; Regel[9834]:=Transfor`m`T9834; Regel[9831]:=Transfor`m`T9831; Regel[2191]:=Transfor`m`T2191; Regel[3261]:=Transfor`m`T3261; Regel[3262]:=Transfor`m`T3262; Regel[7691]:=Transfor`m`T7691; Regel[7692]:=Transfor`m`T7692; Regel[9891]:=Transfor`m`T9891; Regel[2110]:=Transfor`m`T2110; Regel[2112]:=Transfor`m`T2112; Regel[2133]:=Transfor`m`T2133; Regel[2134]:=Transfor`m`T2134; Regel[2135]:=Transfor`m`T2135; Regel[2136]:=Transfor`m`T2136; Regel[2137]:=Transfor`m`T2137; Regel[2138]:=Transfor`m`T2138; Regel[2139]:=Transfor`m`T2139; Regel[2140]:=Transfor`m`T2140; Regel[2141]:=Transfor`m`T2141; Regel[2163]:=Transfor`m`T2163; Regel[3235]:=Transfor`m`T3235; Regel[3236]:=Transfor`m`T3236; Regel[3237]:=Transfor`m`T3237; Regel[3240]:=Transfor`m`T3240; Regel[3263]:=Transfor`m`T3263; Regel[3264]:=Transfor`m`T3264; Regel[3267]:=Transfor`m`T3267; Regel[3268]:=Transfor`m`T3268; Regel[2192]:=Transfor`m`T2192; Regel[3238]:=Transfor`m`T3238; Regel[4309]:=Transfor`m`T4309; Regel[4310]:=Transfor`m`T4310; Regel[4312]:=Transfor`m`T4312; Regel[4362]:=Transfor`m`T4362; Regel[4391]:=Transfor`m`T4391; Regel[4331]:=Transfor`m`T4331; Regel[4332]:=Transfor`m`T4332; Regel[5403]:=Transfor`m`T5403; Regel[5468]:=Transfor`m`T5468; Regel[6501]:=Transfor`m`T6501; Regel[6532]:=Transfor`m`T6532; Regel[6533]:=Transfor`m`T6533; Regel[6534]:=Transfor`m`T6534; Regel[7636]:=Transfor`m`T7636; Regel[7637]:=Transfor`m`T7637; Regel[7693]:=Transfor`m`T7693; Regel[7694]:=Transfor`m`T7694; Regel[8731]:=Transfor`m`T8731; Regel[8732]:=Transfor`m`T8732; Regel[9835]:=Transfor`m`T9835; Regel[9836]:=Transfor`m`T9836; Regel[9837]:=Transfor`m`T9837; Regel[9892]:=Transfor`m`T9892; Regel[9893]:=Transfor`m`T9893; Regel[9894]:=Transfor`m`T9894; Regel[111031]:=Transfor`m`T111031; Regel[111032]:=Transfor`m`T111032; End[] Protect[ Trs01, T2103, T2104, T2106, T2107, T2131, T3204, T3205, T3206, T3207, T3217, T4301, T4302, T7631, T7632, T4303, T4304, T7633, T3231, T3232, T3233, T3234, T4306, T7634, T7635, T5401, T9832, T5402, T9833, T6531, T9834, T9831, T2191, T3261, T3262, T7691, T7692, T9891, T2110, T2112, T2133, T2134, T2135, T2136, T2137, T2138, T2139, T2140, T2141, T2163, T3235, T3236, T3237, T3240, T3263, T3264, T3239, T3267, T3268, T2192, T3238, T4309, T4310, T4312, T4362, T4391, T4331, T4332, T5403, T5468, T6501, T6532, T6533, T6534, T7636, T7637, T7693, T7694, T8731, T8732, T9835, T9836, T9837, T9892, T9893, T9894, T111031, T111032, TListe, TransListe ] EndPackage[] If[$VersionNumber>=2.,$Messages=OutputStream["stdout",1],$Messages={"stdout"}];