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

Abstract

The aim of the paper is to relate computational and arithmetic questions about Euler's constant $\gamma$ with properties of the values of the $q$-logarithm function, with natural choice of $q$. By these means, we generalize a classical formula for $\gamma$ due to Ramanujan, together with Vacca's and Gosper's series for $\gamma$, 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.

AmSTeX, 24 pages, submitted for publication

References in corpus (1)

• A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant

Cited by in corpus (8)

• Euler's constant: Euler's work and modern developments
• Vortex Images and q-Elementary Functions
• Summation of Series Defined by Counting Blocks of Digits
• A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant
• On the properties of a sequence concerning binomial coefficients
• Errata and Addenda to Mathematical Constants
• Improved lower bound on generalized Erdos-Ginzburg-Ziv constants
• A note on a curious formula for Euler's constant