Approximations of the generalized-Euler-constant function and the generalized Somos’ quadratic recurrence constant
نویسندگان
چکیده
منابع مشابه
The Generalized-Euler-Constant Function γ(z) and a Generalization of Somos’s Quadratic Recurrence Constant
We define the generalized-Euler-constant function γ(z) = ∑∞ n=1 z n−1 ( 1 n − log n+1 n ) when |z| ≤ 1. Its values include both Euler’s constant γ = γ(1) and the “alternating Euler constant” log 4 π = γ(−1). We extend Euler’s two zeta-function series for γ to polylogarithm series for γ(z). Integrals for γ(z) provide its analytic continuation to C − [1,∞). We prove several other formulas for γ(z...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2153-0