ON A LINEAR FORM FOR CATALAN’S CONSTANT

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.