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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On Watson's quintuple product identity

Authors: M. V. Subbarao and M. Vidyasagar
Journal: Proc. Amer. Math. Soc. 26 (1970), 23-27
MSC: Primary 10.48
Erratum: Proc. Amer. Math. Soc. 29 (1971), 627.
MathSciNet review: 0263770
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Abstract: In 1929, in the course of proving certain results stated by Ramanujan concerning his continued fraction, G. N. Watson proved an identity involving five infinite products and an infinite series. In 1938, Watson proved another identity which again involved five products. Finally in 1961, one more quintuple product identity was established, this time by Basil Gordon. We show here that all these identities are equivalent. Also, with the help of the quintuple product identity and Jacobi's triple product identity, we establish two new identities involving only series.

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Keywords: Identities of Euler, Jacobi's triple product identity, quintuple product identities of Basil Gordon
Article copyright: © Copyright 1970 American Mathematical Society