Binomial Series Involving Harmonic-like Numbers

Abstract

By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm functions will be established, including a conjectured one made recently by Z.-W. Sun.

Keywords

• binomial series
• harmonic number
• Riemann zeta function
• dilogarithm
• polylogarithm