REMAINDER PADÉ APPROXIMANTS FOR THE HURWITZ ZETA FUNCTION

Marc Prévost (1, 2)

1 ULCO - Université du Littoral Côte d'Opale
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

Following our earlier research, we use the method introduced by the author in [9] named Remainder Padé Approximant in [10], 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 provided.

Mots clés: Pad´e approximants; Zeta function; Bernoulli numbers

Domaines: Théorie des nombres [math.NT]

Marc Prévost. REMAINDER PADÉ APPROXIMANTS FOR THE HURWITZ ZETA FUNCTION. 2018. ⟨hal-01862806⟩