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Summary: A certain series associated with
Catalan'sconstant
Victor Adamchik
adamchik@cs.cmu.edu
Carnegie Mellon University
July 12, 2001
Abstract
A parametric class of series generated by integration of com
plete elliptic integrals
È k#0 k# r
t 2 k
k x 2
þþþþþþþþþþþþþþþþþþþþþþþþþþþþþþþ
rk C rv 16 k
is evaluated in closed form. Alternative proofs to results of
Ramanujan and others are given. A particular case of the Saals
chutzian hypergeometric series 4 F 3
r1v is derived.
Keywords: summation, elliptic functions, hypergeometric functions, Catalan's constant
AMS subject classification: 33C, 33E, 11Y
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