A reciprocity theorem for certain hypergeometric series
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- by Bruce C. Berndt and Dimitris Koukoulopoulos PDF
- Proc. Amer. Math. Soc. 137 (2009), 2369-2373 Request permission
Abstract:
A reciprocity theorem for certain infinite series of gamma functions found in Chapter 14 of Ramanujan’s second notebook is proved and generalized.References
- 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
- Bruce C. Berndt, Chapter 14 of Ramanujan’s second notebook, Enseign. Math. (2) 26 (1980), no. 1-2, 1–65. MR 590507
- Bruce C. Berndt, Ramanujan’s notebooks. Part II, Springer-Verlag, New York, 1989. MR 970033, DOI 10.1007/978-1-4612-4530-8
- Srinivasa Ramanujan, Notebooks. Vols. 1, 2, Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904
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@illinois.edu
- Dimitris Koukoulopoulos
- Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
- Email: dkoukou2@math.uiuc.edu
- Received by editor(s): June 10, 2008
- Received by editor(s) in revised form: September 26, 2008
- Published electronically: January 6, 2009
- Additional Notes: The first author’s research was partially supported by grant H98230-07-1-0088 from the National Security Agency.
- Communicated by: Ken Ono
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2369-2373
- MSC (2000): Primary 33C20
- DOI: https://doi.org/10.1090/S0002-9939-09-09777-9
- MathSciNet review: 2495271