On some conjectural series containing binomial coefficients and harmonic numbers

TL;DR

This paper proves eight conjectural series involving binomial coefficients and harmonic numbers using operator methods and hypergeometric series transformations, advancing understanding in number theory.

Contribution

It introduces new proofs for eight conjectural series involving binomial coefficients and harmonic numbers using innovative operator and hypergeometric series techniques.

Findings

Proved eight conjectural series involving binomial coefficients and harmonic numbers.

Applied operator methods and hypergeometric transformations to establish new identities.

Enhanced methods for analyzing series in number theory.

Abstract

Binomial coefficients and harmonic numbers are important in many branches of number theory. With the help of the operator method and several summation and transformation formulas for hypergeometric series, we prove eight conjectural series of Z.-W. Sun containing binomial coefficients and harmonic numbers in this paper.