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

### 8.40 Definitions

8.401 Bessel functions Zv(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 Jv(z), Bessel functions of the second kind Yv(z) (also called Neumann functions and often written Nv(z)), and Bessel functions of the third kind $Hν(1)(z)$ and $Hν(2)(z)$ (also ...

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