# A new approach to hypergeometric transformation formulas

## TL;DR

This paper introduces a novel, unified method for proving transformation formulas of Gauss hypergeometric functions using Jacobi's canonical form, also extending the approach to q-hypergeometric functions.

## Contribution

The paper presents a new, simplified approach to deriving hypergeometric transformation formulas, leveraging Jacobi's canonical form, and explores analogous methods for q-hypergeometric functions.

## Key findings

- Unified proof technique for hypergeometric transformations
- Extension of methods to q-hypergeometric functions
- Simplification of existing proof processes

## Abstract

We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric functions is also studied.