Some results on generating functions.
Spécialisation dans les disques singuliers réguliers
Stokes matrices of hypergeometric integrals
In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by J.-P. Ramis for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between...
Study of a generalized integral operator
Su un integrale definito del prodotto di funzioni di Bessel e di Struve
Su un integrale fondamentale di funzioni di Struve
Successive derivatives and finite expansions involving the H-function of one and more variables
Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.
Sur les fonctions hyperfuchsiennes provenant des séries hypergéométriques de deux variables
Sur quelques équations différentielles linéaires aréolaires spéciales du II ordre
Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere
We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system....
The distributional 1F1-Transform.
The Laplace transform of the modified Bessel function of the second kind.
The number of points on certain families of hypersurfaces over finite fields
The relational translators of the hyperspherical functional matrix.
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into...
Transformation of an infinite series of Fox's H-function
Two dimensional Laplace transforms of generalized hypergeometric functions.
Гипергеометрические функции, связанные с грассманианом
Матричные ряды Лауричеллы и краевые задачи для вырождающихся эллиптических систем.
О решении интегральных уравнений 1-го рода с ядром в виде обобщенной гипергеометрической функции