2003/04/02 by Jonathan Sondow, Wadim Zudilin · 24 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Computer science #Constant (computer programming) #Euler's formula #Hypergeometric function #Logarithm #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Pure mathematics #Ramanujan's sum #Series (stratigraphy) #math.CA #math.NT #msc:11J72 #msc:11Y60 #msc:33C20 #msc:33D15
paper · pdf · doi:10.1007/s11139-006-0075-1
published in The Ramanujan Journal 12(2), 225-244 (Springer Science+Business Media) · AmSTeX, 24 pages, submitted for publication
arxiv created 2003/04/02 · openalex publication_date 2006/10/01 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The aim of the paper is to relate computational and arithmetic questions about Euler's constant γ with properties of the values of the q-logarithm function, with natural choice of q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca's and Gosper's series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler's constant. The main tools are Euler-type integrals and hypergeometric series.