Nombres D’Euler, approximants de Padé et constante de Catalan

  title={Nombres D’Euler, approximants de Pad{\'e} et constante de Catalan},
  author={T. Rivoal},
  journal={The Ramanujan Journal},
  • T. Rivoal
  • Published 2006
  • Mathematics
  • The Ramanujan Journal
RésuméAu moyen d’une méthode d’approximation de Padé introduite par Prévost dans [13], nous construisons des familles d’approximations rationnelles rapidement convergentes vers la constante de Catalan G. Bien que cela ne suffise pas à prouver l’irrationalité de G, nous montrons le lien inattendu avec la méthode hypergéométrique récemment mise en avant dans l’étude diophantienne des fonction ζ de Riemann et β de Dirichlet, ce qui nous permet de prouver la ≪ conjecture des dénominateurs ≫ de [17… Expand
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