Some special functions identities arising from commuting operators

TL;DR

This paper explores identities involving special functions derived from commuting properties of certain operators, with implications for mathematical physics and quantum operator analysis.

Contribution

It introduces new identities based on the commutation of generalized weighted differential and Hardy-type operators, expanding the understanding of operator relations in mathematical physics.

Findings

Derived new identities involving special functions

Established commutation relations between differential and Hardy-type operators

Enhanced understanding of operator properties in quantum physics

Abstract

Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of order $k$ and the weighted Hardy-type operator commute we derive a number of new and interesting identities involving some functions of mathematical physics.