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)