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A reciprocity theorem for certain hypergeometric series
Author(s):
Bruce
C.
Berndt;
Dimitris
Koukoulopoulos
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2369-2373.
MSC (2000):
Primary 33C20
Posted:
January 6, 2009
MathSciNet review:
2495271
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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:
-
- 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
 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:
10.1090/S0002-9939-09-09777-9
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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