Generalized product formulas for Whittaker's functions and a novel class of index transforms

TL;DR

This paper develops generalized product formulas and index transforms involving Whittaker's functions, providing inversion formulas and extending classical transforms like Kontorovich-Lebedev with complex indices.

Contribution

It introduces new generalized product formulas for Whittaker's functions and derives novel index transforms with explicit inversion formulas.

Findings

Established generalized product formulas for Whittaker's functions.

Derived inversion formulas for the new index transforms.

Extended classical transforms to complex indices with nonzero real parts.

Abstract

Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms with products of the modified Bessel and Whittaker's functions. For our goals the Kontorovich-Lebedev and Olevskii transforms of a complex index with nonzero real part are involved.