New harmonic number identities with applications

Abstract

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ${\sum }_{k=1}^n{\prod }_{j=1}^r{H}_k(\{1{\}}^{{\lambda }_j})$ when ${\sum }_{j=1}^r{\lambda }_j\le 5$. We apply these identities to the study of two congruences modulo a power of a prime.

References in corpus (2)

• A generalization of Carlitz's congruence
• Congruences involving the reciprocals of central binomial coefficients

Cited by in corpus (3)

• Congruences involving the reciprocals of central binomial coefficients
• Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun
• On some congruences using multiple harmonic sums of length three and four