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Some integrals in Ramanujan's lost notebook
Author(s):
Bruce
C.
Berndt
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2983-2988.
MSC (2000):
Primary 33B15;
Secondary 40A10
Posted:
May 12, 2004
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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.
References:
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- 2.
- B. C. Berndt, Ramanujan's Notebooks, Part I, Springer-Verlag, New York, 1985. MR 86c:01062
- 3.
- B. C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1989. MR 90b:01039
- 4.
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- P. J. Forrester, Extensions of several summation formulae of Ramanujan using the calculus of residues, Rocky Mt. J. Math. 13 (1983), 557-572. MR 85i:40004
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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:
10.1090/S0002-9939-04-07430-1
PII:
S 0002-9939(04)07430-1
Received by editor(s):
February 13, 2003
Posted:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
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