An Infinite Product for egamma via Hypergeometric Formulas for Euler's Constant, gamma
Jonathan Sondow
Abstract
We derive hypergeometric formulas for Euler's constant, gamma. A "by-product" of Thomae's transformation is an infinite product for egamma involving the binomial coefficients. Alternate, non-hypergeometric proofs use a double integral for gamma, the beta integral, and an integral for the digamma function. (I thank P. Sebah, S. Zlobin, and W. Zudilin for valuable suggestions used in the paper.)
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