Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T14:51:28.509Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)