Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order

TL;DR

This paper explores new properties and relations of confluent Heun's functions, introduces novel subclasses, and offers an alternative derivation of related polynomials, advancing the mathematical understanding of these special functions.

Contribution

It presents new relations, subclasses, and an alternative derivation method for confluent Heun's functions and their derivatives.

Findings

Derived novel relations for confluent Heun's functions

Introduced specific new subclasses of these functions

Provided an alternative derivation of confluent Heun's polynomials

Abstract

The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's functions are introduced and studied. A new alternative derivation of confluent Heun's polynomials is presented.