Certain classes of series associated with the Zeta function and multiple gamma functions

AbstractThe authors apply the theory of multiple Gamma functions, which was recently revived in the study of the determinants of the Laplacians, in order to evaluate some families of series involving the Riemann Zeta function. By introducing a certain mathematical constant, they also systematically evaluate this constant and some definite integrals of the triple Gamma function. Various classes of series associated with the Zeta function are expressed in closed forms. Many of these results are also used here to compute the determinant of the Laplacian on the four-dimensional unit sphere S4 explicitly

Multiple Gamma Function and Its Application to Computation of Series

The multiple gamma function $\Gamma_n$, 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, Katz and Sarnak, interest in the multiple gamma function has been revived. This paper discusses some theoretical aspects of the $\Gamma_n$ function and their applications to summation of series and infinite products.Comment: 20 pages, Latex, uses kluwer.cls, will appear in The Ramanujan Journa

New identities involving q-Euler polynomials of higher order

In this paper we give new identities involving q-Euler polynomials of higher order.Comment: 11 page