ellippy.legendre.ellippiinc_bulirsch#

ellippy.legendre.ellippiinc_bulirsch(n, phi, m)[source]#

Computes incomplete elliptic integral of the third kind using the Bulirsch algorithm.

This is typically about 2x as fast as the standard implementation for non-PV cases and m < 1 cases, while maintaining similar accuracy. Otherwise, it delegates to ellippiinc().

Parameters:

n (ArrayLike) – Characteristic. n ∈ ℝ, n ≠ 1.
phi (ArrayLike) – Amplitude angle (φ) in radians. φ ∈ ℝ.
m (ArrayLike) – Elliptic parameter. m ∈ ℝ.

Returns:

Scalar or numpy.ndarray broadcast from n, phi, and m.

Notes

See ellippiinc() for definitions, domains, and relationships.

References

Carlson, B. C. “DLMF: Chapter 19 Elliptic Integrals.” Accessed February 19, 2025. https://dlmf.nist.gov/19.
Pornsiriprasert, Sira. Ellip: Elliptic Integrals for Rust. V. 0.5.1. Released October 10, 2025. https://docs.rs/ellip/0.5.1/ellip/index.html.