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Two entries on bilateral hypergeometric series in Ramanujan's lost notebook


Authors: Bruce C. Berndt and Wenchang Chu
Journal: Proc. Amer. Math. Soc. 135 (2007), 129-134
MSC (2000): Primary 33C20
DOI: https://doi.org/10.1090/S0002-9939-06-08553-4
Published electronically: June 19, 2006
MathSciNet review: 2280181
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Abstract | References | Similar Articles | Additional Information

Abstract: Two entries of bilateral sums in Ramanujan's lost notebook are confirmed by means of Dougall's bilateral series identities with one of them being corrected.


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

  • 1. George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999. MR 1688958
  • 2. J. Dougall, On Vandermonde's theorem and some more general expansions, Proc. Edinburgh Math. Soc. 25 (1907), 114-132.
  • 3. M. E. Horn, Bilateral binomial theorem, SIAM Problem 03-001 (2003).
  • 4. Srinivasa Ramanujan, The lost notebook and other unpublished papers, Springer-Verlag, Berlin; Narosa Publishing House, New Delhi, 1988. With an introduction by George E. Andrews. MR 947735
  • 5. Lucy Joan Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966. MR 0201688

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Additional Information

Bruce C. Berndt
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: berndt@math.uiuc.edu

Wenchang Chu
Affiliation: Dipartimento di Matematica, Università degli Studi di Lecce, Lecce-Arnesano P. O. Box 193, 73100 Lecce, Italy
Email: chu.wenchang@unile.it

DOI: https://doi.org/10.1090/S0002-9939-06-08553-4
Received by editor(s): July 23, 2005
Published electronically: June 19, 2006
Additional Notes: The first author’s research was partially supported by grant MDA904-00-1-0015 from the National Security Agency.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society