model.dimnet_basis_util

Jn(r, n)

Numerical spherical bessel functions of order n.

Jn_zeros(n, k)

Compute the first k zeros of the spherical bessel functions up to order n (excluded).

spherical_bessel_formulas(n)

Computes the sympy formulas for the spherical bessel functions up to order n (excluded).

bessel_basis(n, k)

Compute the sympy formulas for the normalized and rescaled spherical bessel functions up to order n (excluded) and maximum frequency k (excluded).

sph_harm_prefactor(l, m)

Computes the constant pre-factor for the spherical harmonic of degree l and order m.

Parameters:

• l (int) – \(l>=0\)

• m (int) – \(-l<=m<=l\)

associated_legendre_polynomials(l, zero_m_only=True)

Computes sympy formulas of the associated legendre polynomials up to order l (excluded).

real_sph_harm(l, zero_m_only=True, spherical_coordinates=True)

Computes formula strings of the the real part of the spherical harmonics up to order l (excluded).

Variables are either cartesian coordinates x,y,z on the unit sphere or spherical coordinates phi and theta.