arXiv subjects

Jorge Antonio González Layja

Publications and source records attributed to Jorge Antonio González Layja.

4 recordsLinked to original sources

arXiv2026

Integral Representations for Multiple Apéry-Like Series

We derive integral representations for six families of multiple Apéry-like series using repeated integration by parts and Fourier expansions. The resulting formulas are expressed in terms of polylogarithms, Legendre chi functions, and inverse tangent integrals. As applications, we recover several known evaluations as special cases of our results, expressed in terms of Dirichlet eta, beta, and lambda functions. In addition, we obtain a new identity expressing a family of such series as linear combinations of products of Dirichlet eta values.

math.NT↗

arXiv2026

On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums

We evaluate, by elementary means, a new family of Apéry-like series involving multiple $t$-harmonic star sums of even weight. Using trigonometric expansions, inverse tangent integrals, and binomial recurrences, we obtain explicit closed-form evaluations of these series as finite alternating sums of products of Dirichlet beta values. Several explicit examples are derived as corollaries.

math.NT↗

arXiv2026

Closed-Form Evaluation of Two Apéry-Like Series of Weight 4

This paper presents closed-form evaluations of two new Apéry-like series of weight $4$ that involve harmonic numbers of the form $H_{2k}$. Several key results are derived and subsequently used to establish connections to the main series.

math.NT↗

arXiv2025

Evaluating Six Apéry-like Series of Weight $5$

The main objective of this paper is to evaluate six new Apéry-like series of weight $5$ in closed form. These series involve harmonic numbers and exhibit the characteristic reciprocal central binomial coefficient structure. Generating functions for the inverse sine and identities related to harmonic numbers are used to link each series to a variety of integrals containing $\ln \left(\sin \left(x\right)\right)$ and $\ln \left(\cos \left(x\right)\right)$, which are evaluated using a range of methods and identities.

math.CO↗