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

@inproceedings{Sondow2003EulerS,
title={Euler ’ s constant , q-logarithms , and formulas of Ramanujan and Gosper},
author={Jonathan Sondow and W. Zudilin},
year={2003}
}

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. We recall the… CONTINUE READING

An Introduction to the Theory of Infinite Series, 2nd edition, Macmillan, London, 1926

T. Bromwich

1926

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Personal communication

P. Sebah

2002

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Highly Influenced

Ramanujan’s short unpublished manuscript on integrals and series related to Euler’s constant, Constructive, Experimental, and Nonlinear Analysis (Limoges