A derivation of two transformation formulas contiguous to that of Kummer's second theorem via a differential equation approach

TL;DR

This paper offers an alternative proof for two transformation formulas related to Kummer's second theorem for the confluent hypergeometric function, using a differential equation approach.

Contribution

It introduces a novel differential equation method to derive transformation formulas contiguous to Kummer's second theorem.

Findings

Provides an alternative proof for two transformation formulas

Uses differential equations to derive hypergeometric function transformations

Enhances understanding of hypergeometric function properties

Abstract

The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer's second transformation for the confluent hypergeometric function ${}_1F_1$ using a differential equation approach.