Poisson summation formula and Index Transforms

TL;DR

This paper investigates summation and integral formulas related to index transforms, focusing on formulas involving the second index of the Whittaker function, expanding the theoretical understanding of these mathematical tools.

Contribution

It introduces new summation and integral formulas associated with index transforms and the second index of the Whittaker function, building on prior work.

Findings

Derived new summation formulas for the second index of the Whittaker function

Established integral formulas related to index transforms

Extended the theoretical framework for index transform analysis

Abstract

Following the work of the second author, a class of summation formulas attached to index transforms is studied in this paper. Our primary results concern summation and integral formulas with respect to the second index of the Whittaker function $W_{\mu,\nu}(z)$.