Discrete index Whittaker transforms

TL;DR

This paper introduces and studies discrete versions of the index Whittaker transform, providing new inversion formulas for functions and sequences involving Whittaker functions with complex parameters.

Contribution

It develops discrete analogs of the index Whittaker transform and derives inversion formulas, expanding the mathematical tools available for analysis involving Whittaker functions.

Findings

Introduces discrete index Whittaker transforms.

Establishes inversion formulas for these transforms.

Provides analytical tools for functions involving Whittaker functions.

Abstract

Discrete analogs of the index Whittaker transform are introduced and investigated. It involves series and integrals with respect to a second parameter of the Whittaker function $W_{\mu, {i n} }(x), \ x >0, \ \mu \in \mathbb{R}, \ n \in \mathbb{N}, \ i $ is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established.