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

DOI10.1007/s11139-006-0075-1zbMath1132.11056arXivmath/0304021OpenAlexW2125109218WikidataQ56137975 ScholiaQ56137975MaRDI QIDQ861562

Wadim Zudilin, Jonathan Sondow

Publication date: 29 January 2007

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0304021

zbMATH Keywords

hypergeometric seriesirrationalityEuler constant

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Irrationality; linear independence over a field (11J72) Evaluation of number-theoretic constants (11Y60)

Related Items (10)

Criteria for irrationality of generalized Euler's constant ⋮ Concerning an infinite series of Ramanujan related to the natural logarithm ⋮ Unnamed Item ⋮ Summation of series defined by counting blocks of digits ⋮ Hydrodynamic limit for the \(d\)-facilitated exclusion process ⋮ Legendre modified moments for Euler's constant ⋮ Arithmetical properties of some series with logarithmic coefficients ⋮ A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler’s constant ⋮ Series and product representations for some mathematical constants ⋮ Euler’s constant: Euler’s work and modern developments

Cites Work

• Unnamed Item
• Unnamed Item
• Approximate formulas for some functions of prime numbers
• On the irrationality of \(\sum (1/(q^ n+r))\)
• Criteria for irrationality of Euler’s constant

This page was built for publication: Euler's constant, \(q\)-logarithms, and formulas of Ramanujan and Gosper