Dixon’s F23(1)-series and identities involving harmonic numbers and the Riemann zeta function

Dixon’s classical summation theorem on F23(1)-series is reformulated as an equation of formal power series in an appropriate variable xx. Then by extracting the coefficients of xmxm, we establish a general formula involving harmonic numbers and the Riemann zeta function. Several interesting identities are exemplified as consequences, including one of the hardest challenging identities conjectured by Weideman (2003).