The Journal of the Indian Mathematical Society

Remy Y. Denis ¹, S. N. Singh ², S. P. Singh ²

Affiliations
1 Department of Mathematics, Gorakhpur University, Gorakhpur, IN
2 Department of Mathematics, T. D. P. G. College, Jaunpur, IN

Abstract

In this paper we establish a very general transformation involving basic hypergeometric functions. We deduce a variety of transformations as its special case. We also deduce certain interesting summatiuon for q-series.

Keywords

Basic Hypergeometric Functions, Transformation of Basic Hypergeometric Functions and Q-Series.

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Remy Y. Denis ¹, S. N. Singh ², S. P. Singh ²

Affiliations
1 Department of Mathematics, University of Gorakhpur, Gorakhpur-273009, IN
2 Department of Mathematics, T. D. P. G. College, Jaunpur-222002, IN

Abstract

In this paper, making use of the most generalized form of Bailey's Lemma due to Andrews, an attempt has been made to establish certain double series identities.

Keywords

Double Series Identities, Bailey's Lemma, Multiple Series, Summation Formula.

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Remy Y. Denis ¹, S. N. Singh ², S. P. Singh ²

Affiliations
1 Department of Mathematics, Gorakhpur University, Gorakhpur, (U.P.), IN
2 Department of Mathematics, T.D.P.G. College, Jaunpur, (U.P.), IN

Abstract

Making use of Bailey’s transform and certain known sums of partial series, an attempt has been made to establish certain transformations of poly-basic hypergeometric series.

Keywords

Transform, Partial Sum, Truncated Series.

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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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