xnn.gnn.featurizers.spherical_bessel.zonal_harmonics#

xnn.gnn.featurizers.spherical_bessel.zonal_harmonics(l_max, cos_alpha)[source]#

The m = 0 real spherical harmonics Y_l^0 of a polar angle.

Parameters:

l_max (int) – Highest degree.
cos_alpha (Tensor) – Cosine of the polar angle, any shape.

Returns:

Y_l^0(alpha) = sqrt((2l+1) / 4pi) P_l(cos alpha) for l = 0 .. l_max along a new last axis, shape (..., l_max + 1), in the dtype of cos_alpha. The Legendre polynomials come from the three-term recurrence, evaluated in float64.

Return type:

Tensor