# scipy.special.i0

scipy.special.i0(x) = <ufunc 'i0'>

  Modified Bessel function of order 0.

  Defined as,

  \[I_0(x) = \sum_{k=0}^\infty \frac{(x^2/4)^k}{(k!)^2} = J_0(\imath x),\]

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

  Parameters
    x array_like

      Argument (float)

  Returns
    I ndarray

      Value of the modified Bessel function of order 0 at x.

  See also

  `iv`
  `i0e`

  Notes

  The range is partitioned into the two intervals [0, 8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

  This function is a wrapper for the Cephes [1] routine `i0`.

  References

  1

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

scipy.special.y1 scipy.special.i0e