Symbolic Computation Group

The multiple gamma function G_{n}, defined by a recurrence-functional equation as a generalization of the Euler gamma function, was originally introduced by Kinkelin, Glaisher, and Barnes around 1900. Today, due to the pioneer work of Conrey, Keating and Sarnak, the interest to the G_{n} function has been revived. Sarnak conjectured the idea that zeros of certain "zeta functions" (L-functions) can be understood in terms of the distribution of eigenvalues from classes of random matrices. It has been shown that the G_{2} function naturally appears there as a closed representation for statistical averages. In this talk I present some theoretical aspects of the multiple gamma function and their application to computation of sums, products and integrals.