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Special values of the hypergeometric series III

Published online by Cambridge University Press:  30 September 2002

G. S. JOYCE  and
I. J. ZUCKER
G. S. JOYCE
Affiliation:
Wheatstone Physics Laboratory, King's College, Strand, London WC2R 2LS.
I. J. ZUCKER
Affiliation:
Wheatstone Physics Laboratory, King's College, Strand, London WC2R 2LS.
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Abstract

In two previous papers [7, 10] the algebraic and transcendental values of the Gauss hypergeometric series

F(a, b; c; z) = 1+abcz1!+a(a+1)b(b+1)c(c+1)z22!+… (1·1)

were investigated, for various real rational parameters a; b; c and algebraic and rational values of z ∈ (0, 1), by applying the singular values of the complete elliptic integral of the first kind K(k) to certain classical F transformation formulae, where k denotes the modulus. Our main aim in the present paper is to use similar methods to determine the special values of (1·1) for the case a = 112, b = 712 and c = 23.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 2 , September 2002 , pp. 213 - 222
Copyright
2002 Cambridge Philosophical Society

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