New inequalities for some generalized Mathieu type series and the Riemann zeta function
نویسندگان
چکیده
منابع مشابه
Some Identities for the Riemann Zeta-function
Several identities for the Riemann zeta-function ζ(s) are proved. For example, if s = σ + it and σ > 0, then ∞ −∞ (1 − 2 1−s)ζ(s) s 2 dt = π σ (1 − 2 1−2σ)ζ(2σ). Let as usual ζ(s) = ∞ n=1 n −s (ℜe s > 1) denote the Riemann zeta-function. The motivation for this note is the quest to evaluate explicitly integrals of |ζ(1 2 + it)| 2k , k ∈ N, weighted by suitable functions. In particular, the prob...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2018
ISSN: 1846-579X
DOI: 10.7153/jmi-2018-12-13