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Results in Mathematics

, 74:51 | Cite as

Remainder Padé Approximants for the Hurwitz Zeta Function

  • Marc PrévostEmail author
Article

Abstract

Following our earlier research, we use the method introduced by the author in Prévost (J Comput Appl Math 67(2):219–235, 1996) named Remainder Padé Approximant in Prévost (Constr Approx 25(1):109–123, 2007), 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 \(\zeta (2)\) and \(\zeta (3)\) are provided.

Keywords

Padé approximants zeta function bernoulli numbers 

Mathematics Subject Classification

Primary 41A21 Secondary 41A28 11J72 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LMPA Joseph Liouville, Centre Universitaire de la Mi-VoixCalais CedexFrance

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