Generating Functions for Binomial Series Involving Harmonic-like Numbers

Abstract

By employing the coefficient extraction method, a class of binomial series involving harmonic numbers will be reviewed through three hypergeometric F12(y2)-series. Numerous closed-form generating functions for infinite series containing binomial coefficients and harmonic numbers will be established, including several conjectured ones.

Keywords

• harmonic numbers
• central binomial coefficient
• hypergeometric series