A q-analogue of Appell’s F₁ function, its integral representation and transformations

Bassam Nassrallah

Vol. 142 (1990), No. 1, 121–134

DOI: 10.2140/pjm.1990.142.121

Abstract

An extension of Askey and Wilson’s q-beta integral is evaluated as a sum of two double series. The formula is then used to find a q-analogue of Appell’s F₁ function via its integral representation as well as q-analogues of transformations of F₁ to another F₁ and F₃ functions.

Mathematical Subject Classification 2000

Primary: 33D60

Secondary: 05A30

Milestones

Received: 4 March 1988

Published: 1 March 1990