# scipy.interpolate.pade

scipy.interpolate.pade(an, m, n=None)

  Return Pade approximation to a polynomial as the ratio of two polynomials.

  Parameters:
    an(N,) array_like

      Taylor series coefficients.

    m int

      The order of the returned approximating polynomial q.

    n int, optional

      The order of the returned approximating polynomial p. By default, the order is `len(an)-1-m`.

  Returns:
    p, q Polynomial class

      The Pade approximation of the polynomial defined by an is `p(x)/q(x)`.

  Examples

      >>> import numpy as np
      >>> from scipy.interpolate import pade
      >>> e_exp = [1.0, 1.0, 1.0/2.0, 1.0/6.0, 1.0/24.0, 1.0/120.0]
      >>> p, q = pade(e_exp, 2)

      >>> e_exp.reverse()
      >>> e_poly = np.poly1d(e_exp)

  Compare `e_poly(x)` and the Pade approximation `p(x)/q(x)`

      >>> e_poly(1)
      2.7166666666666668

      >>> p(1)/q(1)
      2.7179487179487181