New ₅F₄ hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π
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🧮 math.NT
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formulashypergeometricmahlermeasuresthree-variabletransformationsestablishedevaluations
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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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