scipy.special.ellipk¶
-
scipy.special.
ellipk
(m) = <ufunc 'ellipk'>¶ Complete elliptic integral of the first kind.
This function is defined as
\[K(m) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{-1/2} dt\]- Parameters
- marray_like
The parameter of the elliptic integral.
- Returns
- Karray_like
Value of the elliptic integral.
See also
Notes
For more precision around point m = 1, use
ellipkm1
, which this function calls.The parameterization in terms of \(m\) follows that of section 17.2 in [1]. 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
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.