Some evaluation of infinite series involving trigonometric and hyperbolic functions

2017/08/06 by Xu, Ce · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.02236

Abstract

In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic trigonometric functions. In particular, we evaluate in closed form certain classes of infinite series containing hyperbolic trigonometric functions, which are related to Gamma functions and π. Finally, some interesting new consequences and illustrative examples are considered.

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• On a Class of Berndt-type Integrals and Related Barnes Multiple Zeta Functions
• A Family of Berndt-Type Integrals and Associated Barnes Multiple Zeta Functions

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