EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS

We define a new kind of classical digamma function, and establish some its fundamental identities. Then we apply the formulas obtained, extend tools developed by Flajolet Salvy to study more general Euler-type sums. The main results Salvy's paper (Expo. Math. 7(1) (1998), 15-35) are immediate corollaries in this paper. Furthermore, provide parameterized extensions Ramanujan-type identities that involve hyperbolic series. Some interesting consequences illustrative examples considered.