Generalizing Wallis formula

Published 19 Feb 2014 in math.HO | (1402.6577v1)

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.

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D. Huylebrouck

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