Generalizing Wallis’ Formula

DOI10.4169/AMER.MATH.MONTHLY.122.04.371zbMATH Open1342.11099DBLPjournals/tamm/Huylebrouck15arXiv1402.6577OpenAlexW1958289582WikidataQ58120332 ScholiaQ58120332MaRDI QIDQ3450390

Dirk Huylebrouck

Publication date: 5 November 2015

Published in: The American Mathematical Monthly (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1402.6577

zbMATH Keywords

Glaisher-Kinkelin constantEuler-Mascheroni constantWallis' formula

Mathematics Subject Classification ID

Zeta and (L)-functions: analytic theory (11M99) Evaluation of number-theoretic constants (11Y60) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20)

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