Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference2 articles.
1. Transformations of Basic Hypergeometric Functions of any Order
2. Integrals representing general hypergeometric transformations;Slater;Quart. J. Math
Cited by
4 articles.
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1. Evaluation of integrals and the mellin transform;Journal of Soviet Mathematics;1991-05
2. Generalized basic hypergeometric series with unconnected bases;Mathematical Proceedings of the Cambridge Philosophical Society;1967-07
3. Integrals for asymptotic expansions of hypergeometric functions;Proceedings of the American Mathematical Society;1955
4. The evaluation of the basic confluent hypergeometric functions;Mathematical Proceedings of the Cambridge Philosophical Society;1954-07