Generalizing Wallis formula
History and Overview
2014-02-27 v1
Abstract
The present note generalizes a well-known formula for pi/2 named after the English mathematician John Wallis. The two new formulas for infinite products containing the natural numbers and their roots express them using the Euler-Mascheroni constant and the Glaisher-Kinkelin constant. Like Wallis formula, the generalizations are slowly convergent, but their importance is aesthetic as the fomulas probably please the eye of the mathematical beholder.
Keywords
Cite
@article{arxiv.1402.6577,
title = {Generalizing Wallis formula},
author = {D. Huylebrouck},
journal= {arXiv preprint arXiv:1402.6577},
year = {2014}
}
Comments
Accepted for publication, The American Mathematical Monthly, 2015