Generalized basic hypergeometric series with unconnected bases

Author:

Agarwal R. P.,Verma Arun

Abstract

In a series of recent papers Verma and Upadhyay (7,8,9) developed the theory of basic hypergeometric series with two bases q and q½. These investigations were made in an attempt to discover a summation formula for a bilateral basic hypergeometric series 2Ψ2 analogous to that for a 2H2 (cf. Bailey (2,3)) and in finding relations between certain q-infinite products. In one of their papers they mentioned that it did not seem possible to develop the corresponding general theory for basic series with two unconnected bases q and q1. A recent paper by Andrews (1) indicates that transformations between basic hypergeometric series with two unconnected bases can be very interesting and useful in the study of ‘mock’ theta functions and their extensions. Besides this interest, such a theory also enables one to extend the entire existing transformation theory of the generalized basic hypergeometric series.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference9 articles.

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On certain transformations of poly-basic bilateral hypergeometric series;Journal of Computational and Applied Mathematics;2003-11

2. A Method for q-Calculus;Journal of Nonlinear Mathematical Physics;2003

3. A bibasic hypergeometric transformation associated with combinatorial identities of the Rogers-Ramanujan type;Proceedings of the Indian Academy of Sciences - Section A;1995-02

4. Bibasic analystic functions and discrete ‘bibasic’ hypergeometric series;Periodica Mathematica Hungarica;1994-08

5. Summation, transformation, and expansion formulas for bibasic series;Transactions of the American Mathematical Society;1989

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