Note on the Hurwitz-Lerch zeta function of two variables

A number of generalized Hurwitz-Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz-Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz-Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz-Lerch zeta functions than the extended Hurwitz-Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz-Lerch zeta functions than the one considered here, two more generalized settings are provided.