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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a definite integral of a hypergeometric function

Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 120 (1994), 1131-1136
MSC: Primary 33C75
MathSciNet review: 1186995
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Abstract: The connections between the elliptic functions and the hypergeometric series $ _2{F_1}(\tfrac{1} {2},\tfrac{1} {2};1;x)$ is well known and classical. In this note, we investigate its relation with $ _2{F_1}(\tfrac{1} {4},\tfrac{3} {4};1;x)$. We find that it is less ideal than the classical case and discuss the flaws.

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

  • [1] Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1987. A study in analytic number theory and computational complexity; A Wiley-Interscience Publication. MR 877728
  • [2] J. M. Borwein, P. B. Borwein, and F. G. Garvan, Some cubic modular identities of Ramanujan, preprint.
  • [3] F. G. Garvan, Proof of identity of Ramanugan, manuscript.
  • [4] A. Erdélyi, Higher transcendental functions, Vol. 1, McGraw-Hill, New York, 1953.
  • [5] E. T. Whittaker and G. N. Watson, Modern analysis, 4th ed., Cambridge Univ. Press, London and New York, 1958.

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Article copyright: © Copyright 1994 American Mathematical Society