bluemira.magnetostatics._ellipe

Attributes

_P

_Q

Functions

_ellipe(→ float)

E(m) for m >= 0.

ellipe_nb(→ bluemira.magnetostatics._ellipk._FloatOrArray)

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

Module Contents

bluemira.magnetostatics._ellipe._P = (0.0001535525773010133, 0.0025088849216360204, 0.008687868165658896, 0.010735094905607619,...
bluemira.magnetostatics._ellipe._Q = (3.2795489857648585e-05, 0.0010096279267935672, 0.006506094899769275, 0.016886216399331133,...
bluemira.magnetostatics._ellipe._ellipe(m: float) → float

E(m) for m >= 0.

Parameters:

m (float) – Positive scalar.

Returns:

E(m).

Return type:

float

bluemira.magnetostatics._ellipe.ellipe_nb(m: bluemira.magnetostatics._ellipk._FloatOrArray) → bluemira.magnetostatics._ellipk._FloatOrArray

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

Parameters:

m (bluemira.magnetostatics._ellipk._FloatOrArray) – 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)

Return type:

bluemira.magnetostatics._ellipk._FloatOrArray

Notes

\[E(m) = \int_{0}^{\tfrac{\pi}{2}}{(1 - m \sin^2(t)})^{\tfrac{1}{2}} dt\]

[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