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# 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 [R439] routine `i0`.

  References

  [R439] | (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html