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Generalized basic hypergeometric series with unconnected bases

Published online by Cambridge University Press:  24 October 2008

R. P. Agarwal  and
Arun Verma
R. P. Agarwal
Affiliation:
Lucknow University, India
Arun Verma
Affiliation:
Lucknow University, India
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 727 - 734
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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