On some conjectures of Z.-W. Sun involving harmonic numbers

TL;DR

This paper proves ten conjectural series involving harmonic numbers using the digamma function, many of which relate to series expansions of /^2, advancing understanding in number theory.

Contribution

It provides rigorous proofs for ten conjectures of Z.-W. Sun involving harmonic numbers, connecting them to series expansions of /^2.

Findings

Proved ten conjectural series involving harmonic numbers.

Established connections between harmonic series and /^2.

Enhanced understanding of harmonic numbers in number theory.

Abstract

Harmonic numbers are significant in various branches of number theory. With the help of the digamma function, we prove ten conjectural series of Z.-W. Sun involving harmonic numbers. Several ones of them are also series expansions of $\log2/\pi^2$.