Hypergeometric type functions and their symmetries

TL;DR

This paper provides a comprehensive analysis of hypergeometric type functions, exploring their equations, symmetries, recurrence relations, and integral representations to unify understanding across different classes.

Contribution

It offers a systematic and unified discussion of various hypergeometric type equations and their symmetries, including recurrence relations and integral representations.

Findings

Unified framework for hypergeometric equations

Identification of discrete symmetries across classes

Recurrence relations and integral formulas derived

Abstract

We give a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F_1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, we discuss recurrence relations of their solutions, their integral representations and discrete symmetries.