ellippy.legendre.ellipke#
- ellippy.legendre.ellipke(m)[source]#
Computes complete elliptic integrals of the first and second kind K(m) and E(m) simultaneously.
\[\mathrm{ellipke}(m) = \left(K(m),\, E(m)\right)\]- Parameters:
m (
ArrayLike) – Elliptic parameter. m ∈ ℝ, m ≤ 1.- Returns:
A
(K, E)pair of scalars or numpy.ndarray with the same shape as m.- Return type:
tuple[FloatArray, FloatArray] | tuple[float, float]
- Raises:
ValueError – If m > 1 or inputs contain NaN.
Special Cases
ellipke(0) = (π/2, π/2)
ellipke(1) = (∞, 1)
ellipke(-∞) = (0, ∞)
Related Functions
K(m) = ellipk(m)
E(m) = ellipe(m)
Notes
This computes K(m) and E(m) simultaneously, which is faster than computing them separately.
The elliptic modulus k is frequently used instead of the parameter m, where k² = m.
References
Pornsiriprasert, Sira. Ellip: Elliptic Integrals for Rust. V. 1.2.0. Released October 2, 2026. https://docs.rs/ellip/1.2.0/ellip/index.html.