bessel_I( *n* , *z* )

The modified Bessel function of the first kind of *z* in SageMath. Defined by

A solution of the differential equation

\[ \frac{d^2 f}{dz^2} + \frac{1}{z} \frac{df}{dz} - \left[ 1 + \frac{n^2}{z^2} \right] f = 0 \]The second linearly independent solution of this equation for integer order is bessel_K.

Plot on the real axis:

Series expansion about the origin:

Special values:

Related functions: bessel_K

Function category: Bessel functions sagemath-docs