The function Q l is given in terms of the Legendre polynomial P l by
1 integral 1 dzP (z) 1 (x +1 ) sum l 1 Ql(x) = - ----l--= -Pl(x)ln ----- - -Pl-j(x)Pj-1(x). 2 - 1 x - z 2 x -1 j=1 j
In the complex plane there is a branch cut from - oo to 1. The first equality is known as the Neumann formula for the Legendre function.