On harmonic binomial series

TL;DR

This paper evaluates binomial series involving harmonic numbers, offering recursion, integral formulas, and examples, with applications across number theory, algorithms, and physics.

Contribution

It introduces new methods for evaluating harmonic binomial series, including recursion relations and integral representations.

Findings

Derived recursion relations for harmonic binomial series

Provided integral representations and explicit examples

Highlighted applications in number theory and physics

Abstract

We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and calculations of theoretical physics, as well as other applications.