Mellin transforms of Whittaker functions

Mellin transforms of p-adic Whittaker functions

Special functions and the Mellin transforms of Laguerre and Hermite functions

We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynom...

Baxter operator and Archimedean Hecke algebra

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gammafunctions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral...

Autoconvolution equations and generalized Mittag-Leffler ‎functions

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

Harmonic Sums and Mellin Transforms up to two–loop Order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions fi(x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two–loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and...