Bessel Functions

Abstract

Bessel’s differential equation reads

$$\displaystyle{ x^{2} \frac{d^{2}y} {dx^{2}} + x\frac{dy} {dx} + (x^{2} - m^{2})y = 0. }$$

We are only interested in solutions for integer m, denoted as J _m , N _m , and H _m ^1, 2.