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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some integrals in Ramanujan's lost notebook


Author: Bruce C. Berndt
Journal: Proc. Amer. Math. Soc. 132 (2004), 2983-2988
MSC (2000): Primary 33B15; Secondary 40A10
Published electronically: May 12, 2004
MathSciNet review: 2063119
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Abstract: On page 199 in his lost notebook, Ramanujan recorded three unusual integral formulas. Two of his assertions are correct, and proofs are given here. His third claim is incorrect, but it is true in a limiting form. The integrals arise from a claim in Ramanujan's ordinary notebooks on the equality of certain integrals and series in which the integrand and the summands are themselves the same function.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07430-1
PII: S 0002-9939(04)07430-1
Received by editor(s): February 13, 2003
Published electronically: May 12, 2004
Additional Notes: The 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 2004 American Mathematical Society