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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Completion of a Gaussian derivation


Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 84 (1982), 311-314
MSC: Primary 10J20; Secondary 05A19
MathSciNet review: 637190
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Abstract | References | Similar Articles | Additional Information

Abstract: The author supplies evaluation of two coefficients of an identity partially derived by Gauss. Several special cases of this identity are then presented, the last of these identities yielding an alternate proof of Ramanujan's theorem concerning divisibility of certain values of the partition function by the modulus 7.


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

  • [1] G. H. Hardy, Ramanujan, Chelsea, New York, 1959.
  • [2] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
  • [3] Percy A. MacMahon, Combinatory analysis, Two volumes (bound as one), Chelsea Publishing Co., New York, 1960. MR 0141605 (25 #5003)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637190-0
PII: S 0002-9939(1982)0637190-0
Keywords: Identities, partition function, triple-product identity
Article copyright: © Copyright 1982 American Mathematical Society