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

@article{Rivoal2006NombresDA,
  title={Nombres D’Euler, approximants de Pad{\'e} et constante de Catalan},
  author={T. Rivoal},
  journal={The Ramanujan Journal},
  year={2006},
  volume={11},
  pages={199-214}
}
  • 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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TLDR
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan’s constant with rational coecients, a second-order dierence equation is obtained and a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it is derived. Expand
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