Certain results associated with the generalized Riemann zeta functions

Abstract

In this paper we derive new (linear and bilateral) generating functions involving certain families of hypergeometric functions and the Riemann zeta function (or the generalized zeta function). A connection with the Lambert transform is given, and a generalized Lambert transform is introduced. An inversion formula of this transform is obtained and its relationship with the generalized zeta function is also depicted.

Keywords

• Riemann zeta function
• generating function
• Hurwitz zeta function
• Lambert transform
• Laguerre polynomials
• Gauss hypergeometric function