The modulus of Whittaker functions

TL;DR

This paper investigates the properties of the modulus of Whittaker functions, deriving completely monotone functions from them using integral representations, thereby enhancing understanding of their mathematical behavior.

Contribution

It introduces new properties of the modulus of Whittaker functions and identifies completely monotone functions expressed in terms of these moduli.

Findings

Identification of completely monotone functions related to |W_{k,m}(z)|

Derivation from integral representations of products of Whittaker functions

Enhanced understanding of the properties of Whittaker functions

Abstract

The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral representation for products of Whittaker functions due to Erd\'elyi (1938).