The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.

Abstract An approach to the generalized Bessel–Maitland function is proposed in present paper. It denoted by $\mathcal{J}_{\nu , \lambda }^{\mu }$ Jν,λμ where $\mu >0$ xmlns:mml="http://www.w3....

in this paper, using a generalized dunkl translation operator, we obtain an analog of titchmarsh's theorem for the dunkl transform for functions satisfying the lipschitz-dunkl condition in $mathrm{l}_{2,alpha}=mathrm{l}_{alpha}^{2}(mathbb{r})=mathrm{l}^{2}(mathbb{r}, |x|^{2alpha+1}dx), alpha>frac{-1}{2}$.

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

B. Roynette, P. ValloisM. Yor (3) 26/05/2008 (1) Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvre les Nancy Cedex (2) Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu Case 188 F 75252 Paris Cedex 05 (3) Institut Universitaire de France Abstract This paper consists of three parts : in the first part, we describe a family of...

In this document the generalized hyperbolic (GH) distribution is explained to the extent which is required to understand the internals of the R package ghyp. Essentially, the density and moment generating functions of the GH distribution and its special cases are provided together with some important properties of the GH family. In addition the algorithm underlying the fitting procedure for the...