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A simple proof of an identity of Ramanujan

Published online by Cambridge University Press:  09 April 2009

M. D. Hirschhorn
Affiliation:
School of Mathematics University of New South WalesKensington, N.S.W. 2033, Australia
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Abstract

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One of Ramanujan's unpublished, unproven identities has excited considerable interest over the years. Indeed, no fewer than four proofs have appeared in the literature. The object of this note is to present yet another proof, simpler than the others, relying only on Jacobi's triple product identity.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1983

References

Andrews, G. E. (1980) ‘Ramanujan's “lost” notebook III: The Rogers-Ramanujan continued fraction’, Dept. of Mathematics Research Report, The Pennsylvania State University.Google Scholar
Bailey, W. N. (1952a) ‘A note on two of Ramanujan's formulae’, Quart. J. Math. Oxford Ser. (2) 3, 2931.CrossRefGoogle Scholar
Bailey, W. N. (1952b) ‘A further note on two of Ramanujan's formulae’, Quart J. Math. Oxford Ser. (2) 3, 158160.CrossRefGoogle Scholar
Darling, H. B. C. (1921) ‘Proofs of certain identities and congruences enunciated by S. Ramanujan’, Proc. London Math. Soc. (2) 19, 350372.CrossRefGoogle Scholar
Hirschhorn, M. D. (1976) ‘Simple proofs of identities of MacMahon and Jacobi’, Discrete Math. 16, 161162.CrossRefGoogle Scholar
Mordell, L. J. (1922) ‘Note on certain modular relations considered by Messrs Ramanujan, Darling and Rogers’, Proc. London Math. Soc. (2) 20, 408416.CrossRefGoogle Scholar