ON A LINEAR FORM FOR CATALAN’S CONSTANT

Print ISSN: 0972-7752 | Online ISSN: | Total Downloads : 333

Volume : 6 , Issue : 2
DOI:
Author :
C. Krattenthaler (Fakult¨at f¨ur Mathematik Universit¨at Wien, ordbergstraße 15, A-1090 Vienna, Austria)
T. Rivoal (Institut Fourier, NRS UMR 5582 Universit´e Grenoble 1, 100 rue des Maths, BP 74, 8402 Saint-Martin d’H`eres cedex, France)

Abstract

It is shown how Andrews’ multidimensional extension of Watson’s transformation between a very-well-poised 8φ7-series and a balanced 4φ3-series can be used to give a straightforward proof of a conjecture of Zudilin and the second author on the arithmetic behaviour of the coefficients of certain linear forms of 1 and Catalan’s constant. This proof is considerably simpler and more stream-lined than the first proof, due to the second author.

Keywords and Phrases

Catalan’s constant, linear forms, hypergeometric series, Andrews’ identity.

A.M.S. subject classification

11J72, 11J82, 33C20.

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