Some integrals in Ramanujan’s lost notebook
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- by Bruce C. Berndt PDF
- Proc. Amer. Math. Soc. 132 (2004), 2983-2988 Request permission
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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Additional Information
- Bruce C. Berndt
- Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
- MR Author ID: 35610
- Email: berndt@math.uiuc.edu
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2983-2988
- MSC (2000): Primary 33B15; Secondary 40A10
- DOI: https://doi.org/10.1090/S0002-9939-04-07430-1
- MathSciNet review: 2063119