The Bessel function of the first kind of z in Math. A solution of the differential equation
\[ \frac{d^2 f}{dz^2} + \frac{1}{z} \frac{df}{dz} + \left[ 1 - \frac{n^2}{z^2} \right] f = 0 \]besselJ( n, x ) — the first five Bessel function of the first kind of real or complex order n of a real or complex number.
Bessel functions of the first kind for both positive (blue) and negative (red) real order
The second linearly independent solution of this equation for integer order is besselY.
Real part on the real axis:
Imaginary part on the real axis:
Real part on the imaginary axis:
Imaginary part on the imaginary axis:
Real part on the complex plane:
Imaginary part on the complex plane:
Absolute value on the complex plane:
Related functions: besselY
Function category: Bessel functions