A generalization of Stirling numbers

Details A generalization of Stirling numbers A generalization of Stirling numbers

1995-02-09

arxiv.org/abs/math/9502217v1

Mathematics

Combinatorics

Scientific paper

We generalize the Stirling numbers of the first kind $s(a,k)$ to the case where $a$ may be an arbitrary real number. In particular, we study the case in which $a$ is an integer. There, we discover new combinatorial properties held by the classical Stirling numbers, and analogous properties held by the Stirling numbers $s(n,k)$ with $n$ a negative integer. On g\'{e}n\'{e}ralise ici les nombres de Stirling du premier ordre $s(a,k)$ au cas o\`u $a$ est un r\'eel quelconque. On s'interesse en particulier au cas o\`u $a$ est entier. Ceci permet de mettre en evidence de nouvelles propri\'et\'es combinatoires aux quelles obeissent les nombres de Stirling usuels et des propri\'et\'es analougues auquelles obeissent les nombres de Stirling $s(n,k)$ o\`u $n$ est un entier n\`egatif.

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