A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the L-functions

The aim of this paper is to construct a unified family of meromorphic functions, which is related to many known functions such as a unified family of partial zeta type functions, a unified family of L-functions, and so on. We investigate and derive many properties of this family of meromorphic functions. Moreover, we compute the residues of this family of meromorphic functions at their poles. We also give some applications and remarks involving this family of meromorphic functions.