Remainder Padé approximants for the Hurwitz zeta function

2017/09/15 by Prévost, Marc
#11J72 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #Primary 41A21 #Secondary 41A28

paper · doi:10.48550/arxiv.1709.05389

Abstract

Following our earlier research, we use the method introduced by the author in \citeprevost1996 named Remainder Padé Approximant in \citerivoalprevost, 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.

Related

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• On the Hurwitz-type zeta function associated to the Lucas sequence
• Aspects of Zeta-Function Theory in the Mathematical Works of Adolf Hurwitz
• La Zeta de Riemann est irrationnelle aux impairs positifs