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A reciprocity theorem for certain hypergeometric series


Authors: Bruce C. Berndt and Dimitris Koukoulopoulos
Journal: Proc. Amer. Math. Soc. 137 (2009), 2369-2373
MSC (2000): Primary 33C20
DOI: https://doi.org/10.1090/S0002-9939-09-09777-9
Published electronically: January 6, 2009
MathSciNet review: 2495271
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. G. E. Andrews, R. A. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999. MR 1688958 (2000g:33001)
  • 2. B. C. Berndt, Chapter $ 14$ of Ramanujan's second notebook, Enseign. Math. (2) 26 (1980), 1-65. MR 590507 (81k:10037)
  • 3. B. C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1989. MR 970033 (90b:01039)
  • 4. S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957. MR 0099904 (20:6340)

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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@illinois.edu

Dimitris Koukoulopoulos
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: dkoukou2@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09777-9
Keywords: Hypergeometric series, Ramanujan's notebooks, gamma function
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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