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Open AccessMathematics

A quasi-theta product in Ramanujan's lost notebook

B. Berndt, H. Chan, A. Zaharescu

2003.6.26MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

DOI: 10.1017/s0305004102006527

tlooto Summary

Ramanujan's lost notebook contains an unusual product formula involving hypergeometric functions and elliptic functions.

Abstract

On page 209 of his lost notebook, Ramanujan records an unusual product formula, reminiscent of a product of theta functions. The formula involves hypergeometric functions and has a connection with elliptic functions. In this paper, we prove the formula, offer some generalizations, and indicate some further connections with Ramanujan's work.

Citation format

BERNDT, B.; CHAN, H.; ZAHARESCU, A. A quasi-theta product in ramanujan's lost notebook. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2003, 135: 11–18.