ON A LINEAR FORM FOR CATALAN’S CONSTANT

Print ISSN: 0972-7752

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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