New Vacca-Type Rational Series for Euler’s Constant γ and Its “Alternating” Analog $$\ln \frac{4}{\pi }$$

DOI10.1007/978-0-387-68361-4_23zbMath1258.11103arXivmath/0508042OpenAlexW1571546164MaRDI QIDQ2996323

Jonathan Sondow

Publication date: 6 May 2011

Published in: Additive Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508042

zbMATH Keywords

generalized Euler constantEuler's constantrational seriesalternating Euler constantbinary expansionsacceleration of seriesVacca's series

Mathematics Subject Classification ID

Numerical summation of series (65B10) Evaluation of number-theoretic constants (11Y60)

Related Items (11)

On Somos' quadratic recurrence constant ⋮ Inequalities and asymptotic expansions related to the generalized Somos quadratic recurrence constant ⋮ Concerning an infinite series of Ramanujan related to the natural logarithm ⋮ Summation of series defined by counting blocks of digits ⋮ Series representations of the remainders in the expansions for certain functions with applications ⋮ On a general inequality related to the generalized-Euler-constant function ⋮ Summation of rational series twisted by strongly \(B\)-multiplicative coefficients ⋮ Approximations of the generalized-Euler-constant function and the generalized Somos' quadratic recurrence constant ⋮ Euler’s constant: Euler’s work and modern developments ⋮ Another Alternating Analogue of Euler’s Constant ⋮ Yet another representation for reciprocals of the nontrivial zeros of the Riemann zeta function

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