Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper

Title: Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper
Creator: Sondow, Jonathan; Zudilin, W.
Relation: The Ramanujan Journal Vol. 12, Issue 2, p. 225-244
Publisher Link: http://dx.doi.org/10.1007/s11139-006-0075-1
Publisher: Springer
Resource Type: journal article
Date: 2006
Description: 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.
Subject: Euler’s constant; q-logarithm; hypergeometric series; Euler’s transform; irrationality
Identifier: http://hdl.handle.net/1959.13/928070
Identifier: uon:10331
Identifier: ISSN:1382-4090
Rights: The final publication is available at www.springerlink.com
Language: eng
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