bluemira.magnetostatics._ellipe
===============================

.. py:module:: bluemira.magnetostatics._ellipe


Attributes
----------

.. autoapisummary::

   bluemira.magnetostatics._ellipe._P
   bluemira.magnetostatics._ellipe._Q


Functions
---------

.. autoapisummary::

   bluemira.magnetostatics._ellipe._ellipe
   bluemira.magnetostatics._ellipe.ellipe_nb


Module Contents
---------------

.. py:data:: _P
   :value: (0.0001535525773010133, 0.0025088849216360204, 0.008687868165658896, 0.010735094905607619,...


.. py:data:: _Q
   :value: (3.2795489857648585e-05, 0.0010096279267935672, 0.006506094899769275, 0.016886216399331133,...


.. py:function:: _ellipe(m: float) -> float

   E(m) for m >= 0.

   :param m: Positive scalar.

   :returns: E(m).


.. py:function:: ellipe_nb(m: bluemira.magnetostatics._ellipk._FloatOrArray) -> bluemira.magnetostatics._ellipk._FloatOrArray

   Complete elliptic integral of the second kind, E(m).

   :param m: Parameter(s) of the elliptic integral. Values m > 1 return NaN. Can be a float
             or an NDArray. If an array, the function is executed elementwise.

   :returns: E(m)

   .. rubric:: Notes

   .. math::
       E(m) = \int_{0}^{\tfrac{\pi}{2}}{(1 - m \sin^2(t)})^{\tfrac{1}{2}} dt

   [ellipe_1]_

   Implementation based on Scipy's XSF implementation [ellipe_3]_ of the Cephes C
   library [ellipe_2]_ (MIT licensed) - with help from Claude to translate the C
   into Python.

   .. [ellipe_1] Abramowitz, M., and I. A. Stegun. Handbook of Mathematical Functions.
                 Dover Publications, 1965.
   .. [ellipe_2] Moshier, S. L. (2000). Cephes Math Library Release 2.8.
                 http://www.netlib.org/cephes
   .. [ellipe_3] https://github.com/scipy/xsf/blob/a4e89b2aa684ed63f63e5ece79b916e1f0fe619b/include/xsf/cephes/ellpe.h