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q-Series Identities and Reducibility of Basic Double Hypergeometric Functions

Published online by Cambridge University Press:  20 November 2018

H. M. Srivastava  and
V. K. Jain
H. M. Srivastava
Affiliation:
University of Victoria, Victoria, British Columbia
V. K. Jain
Affiliation:
Bareilly College, Bareilly, Uttar Pradesh, India
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For real or complex q, |q| < 1, let

(1.1)

for arbitrary λ and μ, so that

(1.2)

and

(1.3)

Define, as usual, a generalized q-hypergeometric function by (cf. [26, Chapter 3]; see also [18])

(1.4)

where, for convergence, |q| < 1 and |z| < ∞ when r is a positive integer, or |z| < 1 when r = 0, provided that no zeros appear in the denominator.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 1 , 01 February 1986 , pp. 215 - 231
Copyright
Copyright © Canadian Mathematical Society 1986

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