On Watson’s quintuple product identity
HTML articles powered by AMS MathViewer
- by M. V. Subbarao and M. Vidyasagar PDF
- Proc. Amer. Math. Soc. 26 (1970), 23-27 Request permission
Erratum: Proc. Amer. Math. Soc. 29 (1971), 627.
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.References
- George E. Andrews, A simple proof of Jacobi’s triple product identity, Proc. Amer. Math. Soc. 16 (1965), 333–334. MR 171725, DOI 10.1090/S0002-9939-1965-0171725-X
- B. Gordon, Some identities in combinatorial analysis, Quart. J. Math. Oxford Ser. (2) 12 (1961), 285–290. MR 136551, DOI 10.1093/qmath/12.1.285 G. N. Watson, Theorems stated by Ramanujan (VII): Theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48. —, Ramanujan’s Vertumung über Zerfallungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 26 (1970), 23-27
- MSC: Primary 10.48
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263770-2
- MathSciNet review: 0263770