Dixon’s -series and identities involving harmonic numbers and the Riemann zeta function

Dixon’s classical summation theorem on F 2 3 ( 1 ) -series is reformulated as an equation of formal power series in an appropriate variable x . Then by extracting the coefficients of x m , 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).