English

The iterated logarithmic algebra II: Sheffer sequences

Combinatorics 2016-09-06 v1

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.

Keywords

Cite

@article{arxiv.math/9502220,
  title  = {The iterated logarithmic algebra II: Sheffer sequences},
  author = {Daniel E. Loeb},
  journal= {arXiv preprint arXiv:math/9502220},
  year   = {2016}
}