Mellin transforms of Whittaker functions

Mellin transforms of Whittaker functions

In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We determine the possible poles.

Mellin transforms of p-adic Whittaker functions

Mellin Transforms: Harmonic Sums

My assignment is going to introduce the Mellin transform and its application on harmonic sums [1]. Hjalmar Mellin(1854-1933, [2] for a summary of his works) gave his name to the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete prob...

Harmonic Sums and Mellin Transforms

with n0 ≡ N. The finite harmonic sums form classes which are given by their transcendentality t = ∑m l=1 |kl|. This term was chosen to characterize the behavior of these sums for N → ∞. In this case the values of the sums, if existing, are described by a transcendental number of rank t, i.e. log 2, ζ(2), ζ(3) or log 2·ζ(2), etc. for t = 1, 2, 3, ... All harmonic sums have a linear representatio...

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...