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

Sondow, Jonathan and Zudilin, Wadim (2006) Euler�s constant, q-logarithms, and formulas of Ramanujan and Gosper. The Ramanujan Journal, 12 (2). pp. 225-244.

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Euler�s constant, q-logarithm, hypergeometric series, Euler�s transform, irrationality
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1178

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