Une généralisation des théorèmes de MM. Picard-Nevanlinna sur les fonctions méromorphes

Sur une Généralisation des Coefficients Binomiaux

We prove a recent conjecture of Lassalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to the fundamental problem of calculating the linearization coefficients for binomial coefficients.

L’inclinaison Moyenne Des Orbites Des Comètes Sur La Figure De La Terre Et Sur Les Fonctions

One of the most extraordinary phenomena which the system of the world offers to us is the movement of the planets and of their satellites in the same sense and very nearly in the same plane; if we picture to ourselves in fact all these stars describing from west to east some nearly circular orbits and very little inclined to the ecliptic, while the comets seem to be moved indifferently in every...

Sur Le Développement Spectral De La Formule Des Traces D’arthur-selberg Sur Les Corps De Fonctions

Une généralisation automorphe des nombres de Stirling

Let [n] be theset {1,2, *.. , n> and CT a given permutation in S,, the symmetric group on [n]. The (unsigned) Stirling numbers of the first kind enumerate the permutations on En] with k cycles and those of the second kind give the number partitions of [n] having k blocks. In this paper we compute the number of permutations on [n] with k cycles and the number of partitions on [n] having k blocks...

Sur les fonctions q-Bessel de Jackson

(About Jackson q-Bessel functions) Laplace transform allows to resolve differential equations in the neighborhood of an irregular singular point. The purpose of the article is to study how to apply a basic Borel– Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson. Connection matrices are obtained between solutions at the origin and solutions at ...