On a linear form for Catalan's constant

Details On a linear form for Catalan's constant On a linear form for Catalan's constant

2008-10-10

arxiv.org/abs/0810.1927v1

South East Asian J. Math. Math. Sci. 6 (No.2) (2008), 3-15

Mathematics

Number Theory

12 pages, AmS-LaTeX

Scientific paper

It is shown how Andrews' multidimensional extension of Watson's transformation between a very-well-poised $_8\phi_7$-series and a balanced $_4\phi_3$-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.

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