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From a Ramanujan-Selberg continued fraction to a Jacobian identity


Author: Hei-Chi Chan
Journal: Proc. Amer. Math. Soc. 137 (2009), 2849-2856
MSC (2000): Primary 05A15, 05A30, 05A40
DOI: https://doi.org/10.1090/S0002-9939-09-09835-9
Published electronically: March 4, 2009
MathSciNet review: 2506441
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Abstract: Jacobi proved an elegant identity involving eight-fold infinite products. In this paper, we give a new proof of this identity. A key ingredient of our proof is an identity satisfied by a Ramanujan-Selberg continued fraction.


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Additional Information

Hei-Chi Chan
Affiliation: Department of Mathematical Sciences, University of Illinois at Springfield, Springfield, Illinois 62703-5407
Email: chan.hei-chi@uis.edu

DOI: https://doi.org/10.1090/S0002-9939-09-09835-9
Keywords: Ramanujan-Selberg continued fraction, Jacobian identity
Received by editor(s): October 9, 2008
Received by editor(s) in revised form: November 24, 2008
Published electronically: March 4, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.