# scipy.special.y0

scipy.special.y0(x) = <ufunc 'y0'>

  Bessel function of the second kind of order 0.

  Parameters
    x array_like

      Argument (float).

  Returns
    Y ndarray

      Value of the Bessel function of the second kind of order 0 at x.

  See also

  `j0`
  `yv`

  Notes

  The domain is divided into the intervals [0, 5] and (5, infinity). In the first interval a rational approximation \(R(x)\) is employed to compute,

  \[Y_0(x) = R(x) + \frac{2 \log(x) J_0(x)}{\pi},\]

  where \(J_0\) is the Bessel function of the first kind of order 0.

  In the second interval, the Hankel asymptotic expansion is employed with two rational functions of degree 6/6 and 7/7.

  This function is a wrapper for the Cephes [1] routine `y0`.

  References

  1

    Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

scipy.special.j1 scipy.special.y1