On the Laurent coefficients of a class of Dirichlet series

The generalized Euler constants for an arithmetic progression have been considered by several authors including D. H. Lehmer, W. E. Briggs, K. Dilcher and S. Kanemitsu as an important generalization of the ordinary Euler-Stieltjes constants. In this paper, answering a problem posed by Kanemitsu, we shall adopt the partial zeta-function, a special case of the Hurwitz zeta-function, as a genuine generating function for the generalized Euler constants and make extensive use of the Hurwitz zeta-function to derive all the preceding results of Dilcher and Kanemitsu in a unified and elucidated manner.