On a linear form for Catalan's constant

Abstract

It is shown how Andrews' multidimensional extension of Watson's transformation between a very-well-poised ${}_8{\varphi }_7$-series and a balanced ${}_4{\varphi }_3$-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.

12 pages, AmS-LaTeX

References in corpus (2)

• A few remarks on linear forms involving Catalan's constant
• Binomial sums related to rational approximations to $\zeta (4)$