Uniform upper bounds and asymptotic expansions for certain index kernels

TL;DR

This paper derives uniform upper bounds and asymptotic expansions for kernels of index transforms related to the Kontorovich-Lebedev operator, including Mehler-Fock, Lebedev, index Whittaker, and Olevskii transforms.

Contribution

It provides new uniform bounds and asymptotic formulas for a class of index kernels, extending previous work on the Kontorovich-Lebedev operator.

Findings

Established uniform upper bounds for index kernels.

Derived asymptotic expansions for these kernels.

Extended results to multiple related transforms.

Abstract

We continue to establish uniform upper bounds and asymptotic expansions for the kernels of the index transforms which were recently developed for the Kontorovich-Lebedev operator. It involves the Mehler-Fock, Lebedev, index Whittaker and Olevskii transforms.