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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: 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] Peter Henrici, A triple product theorem for hypergeometric series, SIAM J. Math. Anal. 18 (1987), no. 6, 1513–1518. MR 911645,
  • [3] H. M. Srivastava and Per W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1985. MR 834385

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Keywords: Hypergeometric functions, Chu-Vandermonde theorem, Appell functions, triple series identity, quadratic and cubic transformations, Pochhammer symbol
Article copyright: © Copyright 1990 American Mathematical Society

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