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
- phiarray_like
amplitude of the elliptic integral.
- marray_like
parameter of the elliptic integral.
- Returns
- Endarray
Value of the elliptic integral.
See also
Notes
Wrapper for the Cephes [1] routine ellie.
Computation uses arithmetic-geometric means algorithm.
The parameterization in terms of \(m\) follows that of section 17.2 in [2]. Other parameterizations in terms of the complementary parameter \(1 - m\), modular angle \(\sin^2(\alpha) = m\), or modulus \(k^2 = m\) are also used, so be careful that you choose the correct parameter.
References
- 1
Cephes Mathematical Functions Library, http://www.netlib.org/cephes/
- 2
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.