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# scipy.special.ellipeinc

`scipy.special.``ellipeinc`(phi, m) = <ufunc 'ellipeinc'>

  Incomplete elliptic integral of the second kind

  This function is defined as

  \[E(\phi, m) = \int_0^{\phi} [1 - m \sin(t)^2]^{1/2} dt\]

  Parameters: | phi : array_like amplitude of the elliptic integral. m : array_like parameter of the elliptic integral.
  Returns: | E : ndarray Value of the elliptic integral.

  See also

  `ellipkm1`
    Complete elliptic integral of the first kind, near m = 1
  `ellipk`
    Complete elliptic integral of the first kind
  `ellipkinc`
    Incomplete elliptic integral of the first kind
  `ellipe`
    Complete elliptic integral of the second kind

  Notes

  Wrapper for the Cephes [R403] routine ellie.

  Computation uses arithmetic-geometric means algorithm.

  References

  [R403] | (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html