Rational approximation to the Hurwitz-Lerch zeta function

The main result of this paper is the construction of new sequences of rational approximations to the Lerch function. This construction is based on a generalization of the “remainder Pade approximants” method introduced by the author in 1996. More recently, this method has been applied, in the form of remainder Pade-type approximants, to the approximation of Stieltjes constants.