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Some Values for the Rogers-Ramanujan Continued Fraction

Published online by Cambridge University Press:  20 November 2018

Bruce C. Bernd  and
Heng Huat Chan
Bruce C. Bernd
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A. e-mail: [email protected]@math.uiuc.edu
Heng Huat Chan
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A. e-mail: [email protected]@math.uiuc.edu
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Abstract

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In his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have been proved by K. G. Ramanathan, using mostly ideas with which Ramanujan was unfamiliar. In this paper, eight of Ramanujan's values are established; four are proved for the first time, while the remaining four had been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identities, which have not been heretofore used for evaluating continued fractions.

Keywords

33D1040A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 5 , 01 October 1995 , pp. 897 - 914
Copyright
Copyright © Canadian Mathematical Society 1995

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