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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Henrici's triple product theorem


Authors: Per W. Karlsson and H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 110 (1990), 85-88
MSC: Primary 33A30
MathSciNet review: 1010802
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Abstract | References | Similar Articles | Additional Information

Abstract: Making use of certain known transformations in the theory of hypergeometric functions, the authors prove a general triple series identity which readily yields Henrici's recent result expressing the product of three hypergeometric $ _0{F_1}$ functions in terms of a hypergeometric $ _2{F_7}$ function.


References [Enhancements On Off] (What's this?)

  • [1] W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc. 28 (1928), 242-254.
  • [2] P. Henrici, A triple product theorem for hypergeometric series, SIAM J. Math. Anal. 18 (1987), 1513-1518. MR 911645 (88k:33006)
  • [3] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian hypergeometric series, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1985. MR 834385 (87f:33015)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1010802-2
PII: S 0002-9939(1990)1010802-2
Keywords: Hypergeometric functions, Chu-Vandermonde theorem, Appell functions, triple series identity, quadratic and cubic transformations, Pochhammer symbol
Article copyright: © Copyright 1990 American Mathematical Society