GENERALIZED MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS

Explicit formulas are given for the expression of multiple-sum zeta functions of the type E(infinity)l(1),...,l(N)=-infinity[a(1)(l(1)-c(1))(2) + ... + a(N)(l(N)-c(N))(2) + M(2)]-(s) where a(i)>0, M(2) greater than or equal to O, i= 1,...,N, in terms of Riemann and Hurwitz zeta functions and in terms of Kelvin functions. Using different analytical continuation methods several formulas, especially useful for different values of the involved parameters, are obtained.