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Journal of the London Mathematical Society 2002 65(2):271-284; doi:10.1112/S0024610701002952
© 2002 by London Mathematical Society
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© The London Mathematical Society

Asymptotic Formulas for Two Continued Fractions in Ramanujan's Lost Notebook

Bruce C. Berndt and Jaebum Sohn

Department of Mathematics 1409 West Green Street, University of Illinois Urbana, IL 61801, USA, berndt{at}math.uiuc.edu
Department of Mathematics 1409 West Green Street, University of Illinois Urbana, IL 61801, USA

Received 12 September 2000. Revision received 22 August 2001.

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.

Department of Mathematics, 231 W 18th Avenue, Ohio State University, Columbus, OH 43210, USA, sohn{at}math.ohio-state.edu


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