A class of identities relating Whittaker and Bessel functions

TL;DR

This paper derives new identities linking Whittaker and Bessel functions for specific complex orders, involving special polynomials satisfying a unique differential equation and expressible via Bessel and hypergeometric functions.

Contribution

It introduces novel identities between Whittaker and Bessel functions, involving special polynomials and a non-hypergeometric differential equation.

Findings

Identities between Whittaker and Bessel functions for complex orders

Polynomials satisfying a fourth order differential equation

Polynomials expressed as combinations of Bessel and hypergeometric functions

Abstract

Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they themselves can be expressed as particular linear combinations of products of modified Bessel and confluent hypergeometric functions.