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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two entries on bilateral hypergeometric series in Ramanujan’s lost notebook
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by Bruce C. Berndt and Wenchang Chu PDF
Proc. Amer. Math. Soc. 135 (2007), 129-134 Request permission


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.
  • 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, DOI 10.1017/CBO9781107325937
  • J. Dougall, On Vandermonde’s theorem and some more general expansions, Proc. Edinburgh Math. Soc. 25 (1907), 114–132.
  • M. E. Horn, Bilateral binomial theorem, SIAM Problem 03-001 (2003).
  • Srinivasa Ramanujan, The lost notebook and other unpublished papers, Springer-Verlag, Berlin; Narosa Publishing House, New Delhi, 1988.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
  • 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
  • MR Author ID: 35610
  • Email:
  • Wenchang Chu
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Lecce, Lecce-Arnesano P. O. Box 193, 73100 Lecce, Italy
  • MR Author ID: 213991
  • Email:
  • 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
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 129-134
  • MSC (2000): Primary 33C20
  • DOI:
  • MathSciNet review: 2280181