The continuous Legendre transform, its inverse transform, and applications.
The Convergence Rates of Expansions in Jacobi Polynomials.
The distributional 1F1-Transform.
The Dunkl transform.
The function and some well-known sequences.
The generalized Airy diffusion equation.
The generating function of ternary trees and continued fractions.
The Hermite polynomials and the Bessel functions from a general point of view.
The hyperspherical functions of a derivative.
The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub.
The Laplace transform of the modified Bessel function of the second kind.
The law of the maximum of a Bessel bridge.
The Lebesgue Constants for Borel Summation of Laplace Series.
The Mehler-Fock transform of general order and arbitrary index and its inversion.
The number of points on certain families of hypersurfaces over finite fields
The Numerical Computation of the Confluent Hypergeometric Function U(a,b,z)
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson Kernel for Heisenberg Polynomials on the Disk.
The properties, inequalities and numerical approximation of modified Bessel functions.
The quantized Jacobi polynomials
The author studies a system of polynomials orthogonal at a finite set of points its weight approximating that of the orthogonal system of classical Jacobi polynomials.