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Berndt-type Integrals: Unveiling Connections with Barnes Zeta and Jacobi Elliptic Functions

Autor: Bradshaw, Zachary P., Vignat, Christophe

We address a class of definite integrals known as Berndt-type integrals, highlighting their role as specialized instances within the integral representation framework of the Barnes-zeta function. Building upon the foundational insights of Xu and Zhao

Externí odkaz: http://arxiv.org/abs/2407.02365

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General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions

Autor: Xu, Ce, Zhao, Jianqiang

In this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums associated with

Externí odkaz: http://arxiv.org/abs/2401.01385

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Reciprocity formulas for certain generalized Hardy-Berndt sums

Autor: He, Yuan

In this paper, we establish some reciprocity formulas for certain generalized Hardy-Berndt sums by using the Fourier series technique and some properties of the periodic zeta function and the Lerch zeta function. It turns out that one of Hardy's reci

Externí odkaz: http://arxiv.org/abs/2401.00774

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Berndt-Type Integrals and Series Associated with Ramanujan and Jacobi Elliptic Functions

Autor: Xu, Ce, Zhao, Jianqiang

In this paper, we evaluate in closed forms two families of infinite integrals containing hyperbolic and trigonometric functions in their integrands. We call them Berndt-type integrals since he initiated the study of similar integrals. We first establ

Externí odkaz: http://arxiv.org/abs/2301.08211

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