Extrait d'une Lettre à M. Hermite, relative à l'application des fonctions elliptiques à la théorie des perturbations.
Extrait d'une lettre de M. Ch. Hermite à M. L. Königsberg sur le développement des fonctions elliptiques suivant les puissances croissantes de la variable.
Factorial study of a certain parametric distribution.
The general theory of factorial analysis of continuous correspondance (FACC) is used to investigate the binary case of a continuous probability measure defined as:T(x,y) = ayn + b, (x,y) ∈ D & n ∈ N = 0, elsewhereWhere n ≥ 0, a and b are the parameters of this distribution, while the domain D is a variable trapezoidal inscribed in the unit square. The trapezoid depends on two parameters α and β.This problem is solved. As special cases of our problem we obtain a complete solution for...
Factorization of the hypergeometric-type difference equation on the uniform lattice.
Finite and infinite series involving MacRobert's E-Function
Finite monodromy of Pochhammer equation
We consider the monodromy group of the Pochhammer differential equation . Let be the reduce equation modulo a prime . Then we show that is finite if and only if has a full set of polynomial solutions for almost all primes .
Finite Rogers-Ramanujan type identities.
First hitting time of the boundary of the Weyl chamber by radial Dunkl processes.
Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc
We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions on a concrete realization of the universal covering group of . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to , and corresponding to the eigenvalue .
Fonctions de Mathieu et fonctions propres de l'oscillateur relativiste
Fonctions généralisées sphériques sur
Fonctions hypergéométriques en plusieurs variables et espaces des modules de variétés abéliennes
Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents
Formulae novae in theoria transcendentium ellipticarum fundamentales.
Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique
A Gutzmer formula for the complexification of a Riemann symmetric space. We consider a complex manifold and a real Lie group of holomorphic automorphisms of . The question we study is, for a holomorphic function on , to evaluate the integral of over a -orbit by using the harmonic analysis of . When is an annulus in the complex plane and the rotation group, it is solved by a classical formula which is sometimes called Gutzmer’s formula. We establish a generalization of it when is...
Fourier transform and distributional representation of the gamma function leading to some new identities.
Fourier transform of .
Fourier-Bessel functions of singular continuous measures and their many asymptotics.
Four-term recurrence relations for hypergeometric functions of the second order. II.
The recent work on four-term recurrence relations for the second order functions of hypergeometric type undertaken by the author is developed from a slightly different point of view also using generating functions. The direction of future prospects is indicated.
Four-term recurrence relations for hypergeometric functions of the second order. I.
Four-term recurrence relations for hypergeometric functions of the second order are deduced from generating functions involving elementary functions. Generalisations are indicated and an example is given of a five-term recurrence for the confluent hypergeometric function.