Evaluation of binomial series with harmonic numbers

TL;DR

This paper introduces a special function linked to the digamma function to evaluate complex series involving binomial coefficients and harmonic numbers in closed form.

Contribution

It presents a novel special function and demonstrates its use in deriving closed-form evaluations of binomial and harmonic series.

Findings

Closed-form expressions for series involving binomial coefficients and harmonic numbers.

Introduction of a new special function related to the digamma function.

Enhanced methods for evaluating series in combinatorics and analysis.

Abstract

We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.