Determination of some generalised Euler sums involving the digamma function

TL;DR

This paper evaluates generalized Euler sums that involve the digamma function, providing new insights into their properties and relationships.

Contribution

It introduces new methods for evaluating Euler sums with the digamma function, extending existing mathematical frameworks.

Findings

Derived explicit formulas for generalized Euler sums

Established connections between Euler sums and special functions

Enhanced understanding of digamma function-related series

Abstract

This paper evaluates some generalised Euler sums involving the digamma function.