qstack.mathutils.xyz_integrals_float

Cartesian integrals for spherical harmonics (float version).

qstack.mathutils.xyz_integrals_float.I23(n, m, k)

Compute an auxiliary integral needed for the integral over the unit sphere.

Parameters:

• n (int)

• m (int)

• k (int)

Returns:

The value of the integral.

Return type:

float

qstack.mathutils.xyz_integrals_float.trinomial(k1, k2, k3)

Compute the trinomial coefficient (k1+k2+k3)! / (k1! * k2! * k3!).

Parameters:

• k1 (int)

• k2 (int)

• k3 (int)

Returns:

The value of the trinomial coefficient.

Return type:

float

qstack.mathutils.xyz_integrals_float.xyz(n, m, k)

Compute the integral of x^2k y^2n z^2m over a unit sphere.

Parameters:

• n (int) – Half of power of y.

• m (int) – Half of power of z.

• k (int) – Half of power of x.

Note

The argument order does not matter.

Returns:

The value of the integral.

Return type:

float