2021 年 75 巻 2 号 p. 295-322
We define a new kind of classical digamma function, and establish some of its fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler-type sums. The main results of Flajolet and Salvy's paper (Expo. Math. 7(1) (1998), 15-35) are immediate corollaries of the main results in this paper. Furthermore, we provide some parameterized extensions of Ramanujan-type identities that involve hyperbolic series. Some interesting new consequences and illustrative examples are considered.
