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Nombres Exponentiels Et Nombres De Bernoulli

  • Jacques Touchard
Extract

Introduction. Les nombres entiers positifs a0, a1, … , an, … définis par la fonction génératrice

et que l'on appelle nombres exponentiels jouent, pour la sommation de certaines séries, un rôle qui rappelle le rôle sommatoire des nombres de Bernoulli. Nous avons rassemblé ici les principales propriétés des nombres an dont plusieurs sont, croyons nous, nouvelles.

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References
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6a. Moser, L. and Wyman, M., An asymptotic formula for the Bell numbers, Trans. Royal Soc. Can. III , 49 (1955), 4954.
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11. Touchard, J., Sur la fonction Gamma, Bull. Soc. Math. 41 (1913), 234242.
12. Touchard, J., Propriétés arithmétiques de certains nombres récurrents, Ann. Soc. Sci. de Bruzelles, 1933, 2131.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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