This differential equation, where *ν* is a real
constant, is called the *modified Bessel's equation*:

Its solutions are known as *modified Bessel functions*.

The *modified Bessel functions of the first kind*, denoted *I*_{ν}(*z*) and *I*_{–ν}(*z*), form a fundamental set of solutions of the modified Bessel's equation. *I*_{ν}(*z*) is defined by

You can compute the modified Bessel functions of the first kind using `besseli`

.

The *modified Bessel functions of the second kind*, denoted *K*_{ν}(*z*), form a second solution independent of *I*_{ν}(*z*) given by