Generalized Bessel function of Type D

TL;DR

This paper expresses the generalized Bessel function for the root system of type D using multivariate hypergeometric series, inspired by Brownian motion in the Weyl chamber of type D.

Contribution

It provides a new representation of the generalized Bessel function of type D through hypergeometric series, linking it to stochastic processes.

Findings

Explicit formula for the generalized Bessel function of type D

Connection established between Bessel functions and Brownian motion in Weyl chambers

Potential applications in harmonic analysis and probability theory

Abstract

We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.