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Two further Ramanujan pairs

Published online by Cambridge University Press:  09 April 2009

Michael D. Hirschhorn
Michael D. Hirschhorn
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

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In a recent article, George E. Andrews considers a generalization of the Rogers-Ramanujan identities involving a pair of infinite sequences of positive integers, which he calls a Ramanujan pair. He lists the known Ramanujan pairs and conjectures that there are no more. The object of this note is to establish the existence of two further Ramanujan pairs.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 1 - 4
Copyright
Copyright © Australian Mathematical Society 1980

References

Andrews, G. E. (1979), ‘An incredible formula of Ramanujan’, Austral. Math. Soc. Gaz. 6, 80–89.Google Scholar
Hirschhorn, M. D. (1976), ‘Simple proofs of identities of MacMahon and Jacobi’, Discrete Math. 16, 161–162.CrossRefGoogle Scholar
Hirschhorn, M.D. (1979), ‘Some partition theorems of the Rogers-Ramanujan type’, J. Combinatorial Theory Ser. A, 27, 33–37.CrossRefGoogle Scholar