Closed-form summations of certain hypergeometric-type series containing the digamma function

Abstract

Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen. 39 3011 - 20) mainly by exploiting already known results and using certain transformation and reduction formulae in the theory of the Kampe de Feriet double hypergeometric function. It is shown here that these, and several other series of this type, can be closed-form summed by simpler and more direct arguments based only on a derivative formula for the Pochhammer symbol and the theory of the digamma ( or.) function and generalized hypergeometric function. In addition, a new reduction formula for the Kamp e de Feriet function F 1:1;0 (1 2;1) [z, z] is obtained.