The Journal of the Indian Mathematical Society

U. B. Singh ¹, S. N. Singh ¹

Affiliations
1 Department of Mathematics and Statistics, Ewing Christian College, Allahabad-211003, IN

Abstract

The object of this paper is to first obtain certain indentities for the product of k-basic hypergeometric series (k>0) and then to establish certain summation formulae in which the sum of k-th power of the terms of the series has been expressed as the k-th power of certain infinite products.

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U. B. Singh ¹

Affiliations
1 Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, IN

Abstract

Twenty-five years back, Andrews [6] obtained a double series expansion for a series containing two independent bases, and deduced a number of mock theta function identities from it. A year later, Agarwal and Verma [3, 4] developed a theory of generalized hypergeometric series with two unconnected bases, and derived some transformation formulas involving such series by using contour integrals and the calculus of residues.

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