The iterated logarithmic algebra II: Sheffer sequences
Daniel E. Loeb
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. Grâce à une généralisation de la théorie de l'algèbre des logarithmes itérés, on definit un analogue logarithmique des suites de polynômes de Sheffer et d'Appell. Quelques exemples d'applications permettent de déduire la formule de Stirling ainsi qu'un version logarithmique de la formule de sommation de Euler--MacLaurin.
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