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An integral of hypergeometric type

Published online by Cambridge University Press:  24 October 2008

L. J. Slater
L. J. Slater
Affiliation:
Girton CollegeCambridge
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Extract

In a recent paper (2) I gave some integrals which represented general transformations of hypergeometric series of both ordinary and basic types. In this paper I give the most general form of this kind of integral, from which all the previously known general basic transformations can be deduced.

In the usual notation for basic series,

where x may be a function of n, for example,

and Π is written for ‘Idem (a; b)' means that the expression immediately preceding is to be repeated with b written in place of a and a written in place of b.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 4 , October 1952 , pp. 578 - 582
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Sears, D. B.Transformations of basic hypergeometric functions of any order. Proc. Lond. math. Soc. (2), 53 (1951), 181–91.Google Scholar
(2)Slater, L. J.Integrals representing general hypergeometric transformations. Quart. J. Math (2) (in course of publication).Google Scholar