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References

  • Amdeberhan, Tewodros; Espinosa, Olivier; Gonzalez, Ivan; Harrison, Marshall; Moll, Victor H.; Straub, Armin. Ramanujan's master theorem. Ramanujan J. 29 (2012), no. 1-3, 103--120. MR2994092
  • Barnes, E. W.: On the theory of the multiple gamma function. Trans. Camb. Philos. Soc. 19, (1904), 374--425.
  • Biane, Philippe; Pitman, Jim; Yor, Marc. Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 4, 435--465 (electronic). MR1848256
  • Chamayou, Jean-Francois; Letac, Gérard. Additive properties of the Dufresne laws and their multivariate extension. J. Theoret. Probab. 12 (1999), no. 4, 1045--1066. MR1729469
  • Dufresne, Daniel. $G$ distributions and the beta-gamma algebra. Electron. J. Probab. 15 (2010), no. 71, 2163--2199. MR2745729
  • Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
  • Forrester, P. J. Log-gases and random matrices. London Mathematical Society Monographs Series, 34. Princeton University Press, Princeton, NJ, 2010. xiv+791 pp. ISBN: 978-0-691-12829-0 MR2641363
  • Fyodorov, Yan V.; Le Doussal, Pierre; Rosso, Alberto. Statistical mechanics of logarithmic REM: duality, freezing and extreme value statistics of $1/f$ noises generated by Gaussian free fields. J. Stat. Mech. Theory Exp. 2009, no. 10, P10005, 32 pp. MR2882779
  • Hubalek, Friedrich; Kuznetsov, Alexey. A convergent series representation for the density of the supremum of a stable process. Electron. Commun. Probab. 16 (2011), 84--95. MR2763530
  • Jacod, Jean; Kowalski, Emmanuel; Nikeghbali, Ashkan. Mod-Gaussian convergence: new limit theorems in probability and number theory. Forum Math. 23 (2011), no. 4, 835--873. MR2820392
  • Katayama, Koji; Ohtsuki, Makoto. On the multiple gamma-functions. Tokyo J. Math. 21 (1998), no. 1, 159--182. MR1630167
  • Kuznetsov, Alexey. On extrema of stable processes. Ann. Probab. 39 (2011), no. 3, 1027--1060. MR2789582
  • Kuznetsov, A.; Pardo, J. C. Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes. Acta Appl. Math. 123 (2013), 113--139. MR3010227
  • Lagarias, J. C.; Rains, E. On a two-variable zeta function for number fields. Ann. Inst. Fourier (Grenoble) 53 (2003), no. 1, 1--68. MR1973068
  • Nikeghbali, Ashkan; Yor, Marc. The Barnes $G$ function and its relations with sums and products of generalized gamma convolution variables. Electron. Commun. Probab. 14 (2009), 396--411. MR2545290
  • Ostrovsky, Dmitry. Mellin transform of the limit lognormal distribution. Comm. Math. Phys. 288 (2009), no. 1, 287--310. MR2491625
  • Ostrovsky, D. Selberg integral as a meromorphic function. Int. Math. Res. Notices, (2012), DOI: 10.1093/imrn/rns170.
  • Ruijsenaars, S. N. M. On Barnes' multiple zeta and gamma functions. Adv. Math. 156 (2000), no. 1, 107--132. MR1800255
  • Selberg, Atle. Remarks on a multiple integral. (Norwegian) Norsk Mat. Tidsskr. 26, (1944). 71--78. MR0018287
  • Shintani, Takuro. A proof of the classical Kronecker limit formula. Tokyo J. Math. 3 (1980), no. 2, 191--199. MR0605088
  • Steutel, Fred W.; van Harn, Klaas. Infinite divisibility of probability distributions on the real line. Monographs and Textbooks in Pure and Applied Mathematics, 259. Marcel Dekker, Inc., New York, 2004. xii+546 pp. ISBN: 0-8247-0724-9 MR2011862
  • Yor, Marc. A note about Selberg's integrals in relation with the beta-gamma algebra. Advances in mathematical finance, 49--58, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2007. MR2359362


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