aspcol.sphericalharmonics.triple_harmonic_integral

aspcol.sphericalharmonics.triple_harmonic_integral(l1, l2, l3, m1, m2, m3)

Integral of the product of three spherical harmonics

Defined as $int_{omega} Y_{l1,m1}(omega) Y_{l2,m2}(omega) Y_{l3,m3}(omega) domega$ where $omega$ is the angle. It is sometimes (in Sympy for example) called gaunt coefficient.

Parameters:

• l1 (int) – Spherical harmonic orders

• l2 (int) – Spherical harmonic orders

• l3 (int) – Spherical harmonic orders

• m1 (int) – Spherical harmonic degrees

• m2 (int) – Spherical harmonic degrees

• m3 (int) – Spherical harmonic degrees

Returns:

integral_value – the value of the triple harmonic integral

Return type:

float