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ASYMPTOTIC FORMULAS FOR TWO CONTINUED FRACTIONS IN RAMANUJAN'S LOST NOTEBOOK

Published online by Cambridge University Press:  24 March 2003

BRUCE C. BERNDT  and
JAEBUM SOHN
BRUCE C. BERNDT
Affiliation:
Department of Mathematics, 1409 West Green Street, University of Illinois, Urbana, IL 61801, USA; [email protected]
JAEBUM SOHN
Affiliation:
Department of Mathematics, 1409 West Green Street, University of Illinois, Urbana, IL 61801, USA; [email protected] Current address: Department of Mathematics, 231 W 18th Avenue, Ohio State University, Columbus, OH 43210, USA; [email protected]
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Abstract

On page 45 of his lost notebook, Ramanujan recorded two asymptotic formulas for two continued fractions involving the Riemann zeta-function and Dirichlet $L$ -functions. The paper proves a more general theorem and derives Ramanujan's claims as a corollary of the theorem.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 271 - 284
Copyright
The London Mathematical Society, 2002

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