A new probability distribution with applications

Mingjin Wang

Vol. 247 (2010), No. 1, 241–255

DOI: 10.2140/pjm.2010.247.241

Abstract

We introduce a new probability distribution, which is useful in the study of basic hypergeometric series. As applications, we give probabilistic derivations of the q-binomial theorem, the q-Gauss summation formula, a new multiple identity, and an extension of the Rogers–Ramanujan identities.

Keywords

probability distribution, basic hypergeometric series, Andrews–Askey integral, Al-Salam–Carlitz polynomials, Lebesgue’s dominated convergence theorem, Tannery’s theorem, Rogers–Ramanujan identities

Mathematical Subject Classification 2000

Primary: 60E05

Secondary: 33D15, 05A10

Milestones

Received: 21 February 2009

Revised: 12 December 2009

Accepted: 14 May 2010

Published: 1 July 2010