A note on a certain class of functions related to Hurwitz zeta function and Lambert transform (Q2719886)

The authors introduce a multivariable function \(\theta_{(p_n)}^{(\mu_n)}(s, a; x_1,\dots, x_n)\) which generalizes the Hurwitz zeta-function. In special cases it gives the Lerch zeta-function, multiple Hurwitz zeta-functions and some others ``shifted'' zeta-functions. The authors obtain multiple-series generating functions involving \(\theta_{(p_n)}^{(\mu_n)}(s, a; x_1,\dots, x_n)\). A generalization of the Lambert transform is introduced, and its relationship with the above multivariable function is also pointed out.