An Infinite Product for e^gamma via Hypergeometric Formulas for Euler's Constant, gamma
Classical Analysis and ODEs
2007-05-23 v1 Number Theory
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.)
Cite
@article{arxiv.math/0306008,
title = {An Infinite Product for e^gamma via Hypergeometric Formulas for Euler's Constant, gamma},
author = {Jonathan Sondow},
journal= {arXiv preprint arXiv:math/0306008},
year = {2007}
}
Comments
5 pages, 1 figure, submitted for publication