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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA |
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Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp
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A new class of series for 1/\pi
by
Heng Huat Chan
National University of Singapore
Coauthors: W.-C. Liaw (National Chung Cheng University, Taiwan), V. Tan (National University of Singapore)
In his famous paper "Modular equations and approximations to p", S. Ramanujan
recorded a total of sixteen elegant series for 1/p, all of which are of the form
|
|
C
p
|
= |
∞
å
k=0
|
Ak(a + bk) Hk, |
|
where C is some algebraic number, a, b, and H are rational numbers and Ak are
quotients of certain rising factorials. Around the eighties, the Chudnovskys and
the Borweins added a few more series of the above type using singular values of
the modular j-invariants. It was then believed that the list of such series (with a, b and H
rational) is complete. In this talk, I will present several new series which are
candidates of this list of simple series for 1/p.
Date received: March 9, 2000
Copyright © 2000 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cadx-63.