scipy.special.ellipeinc¶
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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
Notes
Wrapper for the Cephes [R416] routine ellie.
Computation uses arithmetic-geometric means algorithm.
The parameterization in terms of \(m\) follows that of section 17.2 in [R417]. 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
[R416] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html [R417] (1, 2) Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.