The Fourier transform on quantum Euclidean space.
The function and some well-known sequences.
The generalised ellipsoidal wave equation [0,3,11].
Explicit solutions are obtained of the linear differential equation of the second order with three regular singularities and one irregular singularity of the first type. The behavior at the point at infinity is discussed. An important special case is an algebraic form of the ellipsoidal wave equation.
The generalized Airy diffusion equation.
The generating function of ternary trees and continued fractions.
The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ℓ2(ℤ+) are essentially self-adjoint for |ν| ≥ 1 and have deficiency indices (1, 1) for |ν| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation...
The Hermite polynomials and the Bessel functions from a general point of view.
The Heun equation and the Calogero-Moser-Sutherland system. II: Perturbation and algebraic solution.
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 Legendre Formula in Clifford Analysis
2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.
The Many Limits of Mixed Means. II. The Carlson Sequences.
The Markov-WZ method.
The Mehler-Fock transform of general order and arbitrary index and its inversion.
The Meilin Transform of the Partial Fraction Expansion for 0 (x).
The multiple gamma function and its q-analogue
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the classical limit of the multiple q-gamma function.
The new properties of the theta functions
It is shown, that the function