Remainder Padé approximants for the Hurwitz zeta function

Abstract

Following our earlier research, we use the method introduced by the author in \cite{prevost1996} named Remainder Padé Approximant in \cite{rivoalprevost}, to construct approximations of the Hurwitz zeta function. We prove that these approximations are convergent on the positive real line. Applications to new rational approximations of $ζ(2)$ and $ζ(3)$ are given.