DATE: Tuesday, March 30 (2010), at 4:05pm
PLACE: LIT 305
SPEAKER:
Krishnaswami Alladi
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TITLE:
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A companion to Ramanujan's continued fraction
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ABSTRACT:
We will discuss a companion to the famous
Ramanujan continued fraction. The convergence of this
fraction has to defined in a certain modified sense. But in
doing so, we find that the fraction combines not only the
two celebrated Rogers-Ramanujan identities, but four
other beautiful identities of Rogers that arise along with
the Rogers-Ramanujan identities in Baxter's solution of
the Hard Hexagon model in statistical mechanics. The
modified convergence of the fraction utilizes a modular
relation due to Andrews that connects the six identities.
In this seminar I will discuss the first part of my paper
K. Alladi, "On the modified convergence of some continued
fractions of Rogers-Ramanujan type", J. Comb. Th. A,
65 (1994), 214-245
where the implications of the modified convergence of
some other continued fractions are also presented.
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