Hypergeometric heritage of W.N. Bailey. With an appendix: Bailey's letters to F. Dyson

TL;DR

This paper reviews W.N. Bailey's contributions to hypergeometric functions and their applications in number theory, complemented by historical correspondence with F. Dyson from the 1940s.

Contribution

It provides a comprehensive overview of Bailey's work on hypergeometric functions and includes historical letters, offering both mathematical and historical insights.

Findings

Bailey's hypergeometric functions have significant applications in number theory.

Historical letters reveal the development and collaboration in mathematical research.

The paper highlights Bailey's influence on modern mathematical analysis.

Abstract

We review some of W.N. Bailey's work on hypergeometric functions that found solid applications in number theory. The text is complemented by Bailey's letters to Freeman Dyson from the 1940s.