An Infinite Product for e^gamma via Hypergeometric Formulas for Euler's Constant, gamma

2003/05/31 by Jonathan Sondow, Sondow, Jonathan
Mathematics · #33B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Primary 33C20 #Secondary 11Y60 #math.CA #math.NT #msc:11Y60 #msc:33B15 #msc:33C20

paper · pdf · doi:10.48550/arxiv.math/0306008

5 pages, 1 figure, submitted for publication

arxiv created 2003/05/31 · arxiv updated 2009/11/30

Abstract

We derive hypergeometric formulas for Euler's constant, gamma. A "by-product" of Thomae's transformation is an infinite product for e^gamma 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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