A simplification of the Laplace method for double integrals. Application to the second Appell function.
A triple lacunary generating function for Hermite polynomials.
Advanced determinant calculus.
An expression for the superposition of general algebraic functions in terms of hypergeometric series.
Appell orthogonal polynomials on the unit circle
Approximants de Padé et -dérivation
Asymptotic approximations of integrals: an introduction, with recent developments and applications to orthogonal polynomials.
Bi-axial Gegenbauer functions of the first and second kind
The classical orthogonal polynomials defined on intervals of the real line are related to many important branches of analysis and applied mathematics. Here a method is described to generalise this concept to polynomials defined on higher dimensional spaces using Bi-Axial Monogenic functions. The particular examples considered are Gegenbauer polynomials defined on the interval [-1,1] and the Gegenbauer functions of the second kind which are weighted Cauchy integral transforms over this interval of...
Bilinear generating functions for Laguerre and Lauricella polynomials in several variables
Closed form solutions to generalized logistic-type nonautonomous systems.
Fonctions hypergéométriques en plusieurs variables et espaces des modules de variétés abéliennes
Hyperlogarithmic expansion and the volume of a hyperbolic simplex
Integral representations of generalized Lauricella hypergeometric functions.
Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization...
On the determinant of Gauss-Manin connections and hypergeometric functions of hypersurfaces.
Operators preserving orthogonality of polynomials
Let S be a degree preserving linear operator of ℝ[X] into itself. The question is if, preserving orthogonality of some orthogonal polynomial sequences, S must necessarily be an operator of composition with some affine function of ℝ. In [2] this problem was considered for S mapping sequences of Laguerre polynomials onto sequences of orthogonal polynomials. Here we improve substantially the theorems of [2] as well as disprove the conjecture proposed there. We also consider the same questions for polynomials...
Remarks on orthogonal polynomials with respect to varying measures and related problems.
Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels.
Some generating functions involving the Stirling numbers of the second kind.
Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem.