def Y(L_max,m,s,cos_theta):
"""
Gives spin-wieghted spherical harmonic functions on the Gauss quaduature grid.
Returns an array with shape = ( L_max-L_min(m,s) + 1, len(cos_theta) ).
Parameters
----------
L_max, m,s : int
spherical harmonic parameters.
dm, ds: int
increments in (m,s)
a,b : int
starting Jacobi parameters
da,db: int
increments in (a,b)
"""
a, b = a_and_b(m,s)
N = L_max - L_min(m,s)
phase = (-1)**max(m,-s)
init=phase*jacobi.envelope(a,b,0,0,cos_theta)
return jacobi.recursion(N,a,b,cos_theta,init)
def polynomial(N, k, ell, z, a=alpha):
""" N is max degree of output Jacobi polynomial.
There will be blood if N >> len(z) - ell//2."""
q, m = k + a, ell + 1 / 2
init = np.sqrt(2**(k + 5 / 2)) * jacobi.envelope(q, m, q, 1 / 2, z)
return jacobi.recursion(N, q, m, z, init)
def polynomial(N_max,k,m,z,a=alpha):
q = k + a
N = N_max # - some function of m
init = np.sqrt(2**k)*jacobi.envelope(q,m,q,0,z)
return jacobi.recursion(N,q,m,z,init)