## 8.4–8.5 Bessel Functions and Functions Associated with Them

### 8.40 Definitions

8.401 Bessel functions Z_{v}(z) are solutions of the differential equation

$\frac{{d}^{2}{Z}_{\nu}}{d{z}^{2}}+\frac{1}{z}\frac{d{Z}_{\nu}}{dz}+\left(1-\frac{{\nu}^{2}}{{z}^{2}}\right){Z}_{\nu}=0$

KU 37(1)

Special types of Bessel functions are what are called Bessel functions of the first kind J_{v}(z), Bessel functions of the second kind Y_{v}(z) (also called Neumann functions and often written N_{v}(z)), and Bessel functions of the third kind ${H}_{\nu}^{(1)}(z)$ and ${H}_{\nu}^{(2)}(z)$ (also ...