On some rational zeta series involving $\zeta(2n)$ and binomial coefficients

TL;DR

This paper derives an exact formula for a broad class of rational zeta series involving n and binomial coefficients, expressing them via Hurwitz zeta values, extending previous results.

Contribution

It introduces a new general formula for rational zeta series involving n and binomial coefficients, using derivatives polynomials for the cotangent function.

Findings

Provides an explicit formula for the series in terms of Hurwitz zeta values.

Generalizes previous specific formulas to a broader family.

Uses derivatives polynomials for the cotangent function in the derivation.

Abstract

In this note, we give an exact formula for a general family of rational zeta series involving the coefficient $\zeta(2n)$ in terms of Hurwitz zeta values. This formula generalizes two formulas from a previous paper of the first author. Our method will involve derivatives polynomials for the cotangent function.