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Some theta function identities related to the Rogers-Ramanujan continued fraction
Author(s):
Seung
Hwan
Son
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2895-2902.
MSC (1991):
Primary 33D10;
Secondary 11A55
MathSciNet review:
1458265
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Abstract:
In his first and second letters to Hardy, Ramanujan made several assertions about the Rogers-Ramanujan continued fraction  . In order to prove some of these claims, G. N. Watson established two important theorems about  that he found in Ramanujan's notebooks. In his lost notebook, after stating a version of the quintuple product identity, Ramanujan offers three theta function identities, two of which contain as special cases the celebrated two theorems of Ramanujan proved by Watson. Using addition formulas, the quintuple product identity, and a new general product formula for theta functions, we prove these three identities of Ramanujan from his lost notebooks.
References:
- 1.
- B. C. Berndt, Ramanujan's Notebooks, Part III, Springer-Verlag, New York, 1991. MR 92j:01069
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- 3.
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- 4.
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- 5.
- B. C. Berndt, S.-S. Huang, J. Sohn and S. Son, Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan's lost notebook (preprint).
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Additional Information:
Seung
Hwan
Son
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801
Email:
son@math.uiuc.edu
DOI:
10.1090/S0002-9939-98-04516-X
PII:
S 0002-9939(98)04516-X
Keywords:
Rogers-Ramanujan continued fraction,
Euler's pentagonal number theorem,
Jacobi triple product identity,
quintuple product identity
Received by editor(s):
February 21, 1997
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
1998,
American Mathematical Society
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