Some estimates of the generalized beukers integral with techniques of partial fraction decomposition

TL;DR

This paper derives explicit formulas for the generalized Beukers integral using partial fraction techniques, estimates its rational denominator, and provides bounds for related integrals connected to zeta(5).

Contribution

It introduces a new method to explicitly evaluate the generalized Beukers integral and estimates its rational denominator, advancing understanding of these integrals and their relation to zeta values.

Findings

Explicit expression for the generalized Beukers integral.

Bounds for the rational denominator of the integral.

Estimates for the integral related to ζ(5).

Abstract

In this paper we establish the generalized Beukers integral $I_{m}(a_{1},...,a_{n})$ with some methods of partial fraction decomposition. Thus one obtains an explicit expression of the generalized Beukers integral. Further, we estimate the rational denominator of $I$ and. In the second section of this paper, we provide some estimates of the upper and lower bound of the value $J_{3}$, which involves the generalized Beukers integral and is related to $\zeta(5)$.