The modified Bessel function is the solution of the differential
x2 y '' + x y' - (x2 + n2) y = 0
which is slightly different from the Bessel differential equation that defines the Bessel function.
There are two solutions:
From the modified Bessel function two modified
Kelvin functions kern(x) and kein(x) can be derived, in
the following way:
kern(x) + i kein(x) = e-nπi/2 Kn(x e πi/4)