Certain results associated with the generalized Riemann zeta functions

• R. Raina Rajasthan Agricultural University-India
• H. Srivastava University of Victoria-Canada

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.