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Transformation formula for a double Clausenian hypergeometric series, its \(q\)-analogue, and its invariance group. (English) Zbl 0994.33007

In the notions of H. M. Srivastava and P. W. Karlsson [Multiple Gaussian hypergeometric series (1985; Zbl 0552.33001)] for generalized basic double series \(\varphi^{1,2,2}_{0,2,2}\), the author works out an useful transformation formula for a terminating \(\varphi^{1,2,2,}_{0, 2,2}\) series, giving rise to a transformation (invariance) group. Special cases of the result obtained here provide interesting known results.

MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33D70 Other basic hypergeometric functions and integrals in several variables
33C70 Other hypergeometric functions and integrals in several variables
33C80 Connections of hypergeometric functions with groups and algebras, and related topics

Citations:

Zbl 0552.33001
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References:

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