The iterated logarithmic algebra II: Sheffer sequences
Abstract
An extension of the theory of the Iterated Logarithmic Algebra gives the logarithmic analog of a Sheffer or Appell sequence of polynomials. This leads to several examples including Stirling's formula and a logarithmic version of the Euler-MacLaurin summation formula. Gr\ace \`a une g\'en\'eralisation de la th\'eorie de l'alg\`ebre des logarithmes it\'er\'es, on definit un analogue logarithmique des suites de polyn\omes de Sheffer et d'Appell. Quelques exemples d'applications permettent de d\'eduire la formule de Stirling ainsi qu'un version logarithmique de la formule de sommation de Euler--MacLaurin.
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