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A quasi-theta product in Ramanujan's lost notebook

Published online by Cambridge University Press:  26 June 2003

BRUCE C. BERNDT ,
HENG HUAT CHAN  and
ALEXANDRU ZAHARESCU
BRUCE C. BERNDT
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, U.S.A. e-mail: berndt@math.uiuc.edu
HENG HUAT CHAN
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Dr. 2, Singapore 117543, Republic of Singapore. e-mail: chanhh@math.nus.edu.sg
ALEXANDRU ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, U.S.A. e-mail: zaharesc@math.uiuc.edu
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 1 , July 2003 , pp. 11 - 18
Copyright
2003 Cambridge Philosophical Society

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