Module spherical 

Spherical Bessel and Hankel functions

Direct port of NC_SphericalHankel from NC_3dFunctions.cpp. These functions are critical for FMM translation operators.

Definitions

Spherical Bessel function of first kind:

j_n(x) = √(π/2x) * J_{n+1/2}(x)

Spherical Bessel function of second kind (Neumann):

y_n(x) = √(π/2x) * Y_{n+1/2}(x)

Spherical Hankel function of first kind:

h_n^(1)(x) = j_n(x) + i * y_n(x)

Functions

spherical_bessel_j

Compute spherical Bessel functions j_n(x) for n = 0, 1, …, order-1

spherical_bessel_j_derivative

Compute derivative of spherical Bessel j_n’(x)

spherical_bessel_y

Compute spherical Bessel functions y_n(x) (Neumann functions) for n = 0, 1, …, order-1

spherical_bessel_y_derivative

Compute derivative of spherical Bessel y_n’(x)

spherical_hankel_first_kind

Compute spherical Hankel functions of the first kind h_n^(1)(x) for n = 0, 1, …, order-1