On an identity by Chaundy and Bullard. II. More history

TL;DR

This paper explores the historical origins and mathematical connections of the Chaundy-Bullard identity, tracing its appearances from 1713 to 2008 and linking it to Krawtchouk polynomials.

Contribution

It uncovers earlier instances of the identity and discusses its relationship with Krawtchouk polynomials, expanding the historical and mathematical understanding of the identity.

Findings

Identifies earlier occurrences of the identity in 18th and 19th-century works.

Establishes a connection between the identity and Krawtchouk polynomials.

Provides a comprehensive historical overview of the identity's development.

Abstract

An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. In a paper which appeared in 2008 in Indag. Math. the authors surveyed many aspects of this identity. In the present paper we discuss much earlier occurrences of this identity in works by Hering (1868), de Moivre (1738) and de Montmort (1713). A relationship with Krawtchouk polynomials in work by Greville (1966) is also discussed.