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Rahman, Mizan; Verma, Arun

Quadratic transformation formulas for basic hypergeometric series. (English) Zbl 0767.33011

Trans. Am. Math. Soc. 335, No. 1, 277-302 (1993).
Goursat’s list of quadratic transformation formulas for Gauss’ hypergeometric functions, which is reproduced in “Higher transcendental functions. Vol. I. edited by A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1953; Zbl 0051.303), has turned out to be very useful in many applications. Certain analogues of such formulas for the \(q\)-hypergeometric functions as well as for the hypergeometric functions defined over finite fields have also recently attracted new attention because of their wide applicability, say in representation theory of quantum groups and in the theory of moduli.
The authors displayed explicitly the \(q\)-analogues of all the formulas in the list, complementing the formulas already presented in the book “Basic hypergeometric series” (1990; Zbl 0695.33001) by G. Gasper and M. Rahman. They based the calculations on the formulas for well-poised \(_ 2\varphi_ 1\) and very-well-poised \(_ 8\varphi_ 7\) basic hypergeometric series. Some quadratic transformation formulas of new type relating \(_{10}\varphi_ 9\) with \(_{12}\varphi_{11}\) are also given.
Reviewer: T.Sasaki

Cited in 8 Documents

MSC:

33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Keywords:

quadratic transformation; basic hypergeometric series

Citations:

Zbl 0051.303; Zbl 0695.33001
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Full Text: DOI

References:

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