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Here are some particularly nice examples from math function that show real and imaginary parts of special functions on complex axes and on the complex plane.

**bessel( n, x )** — the first five Bessel function of the first kind of real or complex order

Bessel functions of the first kind for both positive (blue) and negative (red) real order

Bessel function of the first kind

Bessel function of the second kind

Hankel function of the first kind

Hankel function of the second kind

Jacobi delta amplitude function

Proper spherical harmonics in 3D