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

Author(s): Bruce C. Berndt; Wenchang Chu
Journal: Proc. Amer. Math. Soc. 135 (2007), 129-134.
MSC (2000): Primary 33C20
Posted: June 19, 2006
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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:

1.: G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 2000. MR 1688958 (2000g:33001)
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4.: S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988. MR 0947735 (89j:01078)
5.: L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966. MR 0201688 (34:1570)

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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: 10.1090/S0002-9939-06-08553-4
PII: S 0002-9939(06)08553-4
Received by editor(s): July 23, 2005
Posted: 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 of article: Copyright 2006, American Mathematical Society


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