Generating Functions for Bessel Functions
Author:
- Louis WeisnerLWLouis Weisner
- 1 January 1959
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 11, 148-155
Abstract
On replacing the parameter n in Bessel's differential equation 1.1 by the operator y(∂/∂y), the partial differential equation Lu = 0 is constructed, where 1.2 This operator annuls u(x, y) = v(x)yn if, and only if, v(x) satisfies (1.1) and hence is a cylindrical function of order n. Thus every generating function of a set of cylindrical functions is a solution of Lu = 0.It is shown in § 2 that the partial differential equation Lu = 0 is invariant under a three-parameter Lie group. This group is then applied to the systematic determination of generating functions for Bessel functions, following the methods employed in two previous papers (4; 5).Keywords
This publication has 3 references indexed in Scilit:
- Generating Functions for Hermite FunctionsCanadian Journal of Mathematics, 1959
- Group-theoretic origin of certain generating functionPacific Journal of Mathematics, 1955
- AN EXTENSION OF HYPERGEOMETRIC FUNCTIONS (I)The Quarterly Journal of Mathematics, 1943