qstack.mathutils.xyz_integrals_sym¶
Cartesian integrals for spherical harmonics (symbolic version).
- qstack.mathutils.xyz_integrals_sym.I23(n, m, k)[source]¶
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:
sympy.Expr
- qstack.mathutils.xyz_integrals_sym.trinomial(k1, k2, k3)[source]¶
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:
sympy.Expr
- qstack.mathutils.xyz_integrals_sym.xyz(n, m, k)[source]¶
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:
sympy.Expr