Laplace Transform of Spherical Bessel Functions

Spherical Functions and Spherical Laplace Transform on Ordered Symmetric Space

Let G=H be a semisimple globally hyperbolic symmetric space and let ' be a H-spherical function on G=H. We derive an expansion formula for ' similar to the Harish-Chandra formula for spherical functions on a Riemannian symmetric space. We use this result to analytically continuate the spherical functions in the parameters. A functional equation for ' is derived and then used to invert the spher...

Laplace Transform of Products of Bessel Functions: a Visitation of Earlier Formulas

This note deals with the Laplace transforms of integrands of the form xJα (ax) Jβ (bx), which are found in numerous fields of application. Specifically, we provide herein both a correction and a supplement to the list of integrals given in 1997 by Hanson and Puja, who in turn extended the formulas of Eason, Noble and Sneddon of 1956. The paper concludes with an extensive tabulation for particul...

Spherical Bessel functions and explicit quadrature formula

An evaluation of the derivative of spherical Bessel functions of order n + 1 2 at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.

The Calculation of Spherical Bessel Functions and Coulomb Functions

An account is given of the Steed algorithm for calculating Coulomb functions and, as a special case, both spherical Bessel and Riccati–Bessel functions. These functions are needed for boundary-condition matching in scattering problems in Atomic and Nuclear physics. Central to the technique is the evaluation of continued fractions and for this calculation Lentz’s forward method (modified by Thom...

Update of spherical Bessel transform: FFTW and OpenMP