2014/02/19 by Dirk Huylebrouck, Huylebrouck, D.
Physics and Astronomy · #30B50 #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.1402.6577
openalex publication_date 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.