Towards a change of variable formula for "hypergeometrization"

TL;DR

This paper investigates the properties of hypergeometrization, an operator transforming elementary functions into hypergeometric functions, aiming to develop change of variable formulas to facilitate transformations of multivariate hypergeometric functions.

Contribution

It introduces new change of variable formulas for the hypergeometrization operator, enabling advanced transformations of multivariate hypergeometric functions.

Findings

Derived several change of variable formulas for hypergeometrization

Facilitated new transformations for multivariate hypergeometric functions

Enhanced understanding of hypergeometrization operator properties

Abstract

We are going to study properties of "hypergeometrization" -- an operator which act on analytic functions near the origin by inserting two Pochhammer symbols into their Taylor series. In essence, this operator maps elementary function into hypergeometric. The main goal is to produce number of "change of variable" formulas for this operator which, in turn, can be used to derive great number of transform for multivariate hypergeometric functions.