bessel_J( n , z )

The Bessel function of the first kind of z in SageMath. 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_Y.

Plot on the real axis:

Series expansion about the origin:

Special values:

Related functions:   bessel_Y

Function category: Bessel functions sagemath-docs