Log-tangent integrals and the Riemann zeta function

Log-tangent integrals and the Riemann zeta function

We show that integrals involving the log-tangent function, with respect to any square-integrable function on  , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positive integers are discussed. Furthermore, we show a...

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Bibliographic Details
Main Authors: Lahoucine Elaissaoui, Zine El-Abidine Guennoun
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2019-06-01
Series:Mathematical Modelling and Analysis
Subjects:
Riemann zeta function
Hurwitz zeta function
Apéry’s constant
Dirichlet series
log-tangent integrals
harmonic series
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/7445

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