New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/π$

Details New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/π$ New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/π$

2007-04-18

arxiv.org/abs/0704.2438v4

Mathematics

Number Theory

14 Pages

Scientific paper

New relations are established between families of three-variable Mahler
measures. Those identities are then expressed as transformations for the
$_5F_4$ hypergeometric function. We use these results to obtain two explicit
$_5F_4$ evaluations, and several new formulas for $1/\pi$.

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