Two problems of binomial sums involving harmonic numbers

Abstract

Abstract Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric functions.

Keywords

• Binomial coefficient
• Harmonic number
• Signless Stirling number
• Symmetric function
• Partial fraction decomposition