pg_utils.numerics.special.eval_jacobi_recur_Nmax

pg_utils.numerics.special.eval_jacobi_recur_Nmax(Nmax: int, alpha: float, beta: float, z: ndarray) → ndarray[source]

Evaluate Jacobi polynomials with recurrence relation up to a degree

This functions generates values for Jacobi polynomials from degree 0 up to a specified degree, using recurrence relations.

Parameters:

Nmax (int) – maximum degree, required to be >= 1
alpha (float) – alpha index for Jacobi polynomials
beta (float) – beta index for Jacobi polynomials
z (np.ndarray) – 1-D array of grid points where the Jacobi polynomials are to be evaluated; assumed to be within interval [-1, +1]

Returns:

Array with shape (Nmax + 1, z.size), values for Jacobi polynomials at grid points specified in z.