def __hyp2f1_coefficients(m, N):
    """ Precomputes the coefficients of 1/f(P) = hyp2f1(1, -m, N-m, z).

    m -- a positive integer.
    N -- a positive integer greater than m.
    """
    f = float(m)
    g = N - m
    c = [0] * (m + 1)
    c[0] = 1.0
    k = 1
    while True:
        c[k] = f / g * c[k - 1]
        f -= 1
        if f == 0:
            break
        k += 1
        g += 1
    return c
