EllipPy Documentation

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EllipPy is an elliptic integral library for Python, powered by Rust. All functions support numpy and parallelization. EllipPy features high accuracy and performance. For more details on testing and benchmarks, please refer to [Ellip](p-sira/ellip).

Quick Start

from ellippy import *
import numpy as np

ellipk(m=np.array([0.1, 0.2, 0.3, 0.4, 0.5])) # [1.61244135 1.6596236  1.71388945 1.77751937 1.85407468]

ellippiinc(n=0.1, phi=np.pi / 4, m=0.25) # 0.1003043379500434

cel(kc=0.5, p=0.1, a=1.0, b=-1.0) # -5.2310275365518795

elliprf(x=[0.1, 0.2, 0.3], y=[0.2, 0.4, 0.8], z=[0.3, 0.5, 0.7]) # [2.29880489 1.68455225 1.32157804]

jacobi_zeta(phi=np.pi / 3, m=0.5) # 0.13272240254017148

To install EllipPy, use your preferred package manager:

pip install ellippy

uv add ellippy

Submodules

legendre	Elliptic integral functions in Legendre's form.
bulirsch	Elliptic integral functions in Bulirsch's form.
carlson	Elliptic integral functions in Carlson's form.
misc	Miscellaneous functions related to elliptic integrals.

Legendre’s Integrals

ellippy.legendre

Elliptic integral functions in Legendre’s form.

Complete Elliptic Integrals

Functions

ellipk	Computes complete elliptic integral of the first kind K(m).
ellipe	Computes complete elliptic integral of the second kind E(m).
ellippi	Computes complete elliptic integral of the third kind Π(n | m).
ellipd	Computes complete elliptic integral of Legendre's type D(m).

Incomplete Elliptic Integrals

Functions

ellipf	Computes incomplete elliptic integral of the first kind F(φ | m).
ellipeinc	Computes incomplete elliptic integral of the second kind E(φ | m).
ellippiinc	Computes incomplete elliptic integral of the third kind Π(n; φ | m).
ellippiinc_bulirsch	Computes incomplete elliptic integral of the third kind using the Bulirsch algorithm.
ellipdinc	Computes incomplete elliptic integral of Legendre's type D(φ | m).

Bulirsch’s Integrals

ellippy.bulirsch

Elliptic integral functions in Bulirsch’s form.

Functions

cel	Computes general complete elliptic integral in Bulirsch form cel.
cel1	Computes Bulirsch complete integral of the first kind cel1.
cel2	Computes Bulirsch complete integral of the second kind cel2.
el1	Computes Bulirsch incomplete integral of the first kind el1.
el2	Computes Bulirsch incomplete integral of the second kind el2.
el3	Computes Bulirsch incomplete integral of the third kind el3.

Carlson’s Symmetric Integrals

ellippy.carlson

Elliptic integral functions in Carlson’s form.

Functions

elliprc	Computes Carlson degenerate integral RC.
elliprd	Computes Carlson degenerate integral RD.
elliprf	Computes Carlson symmetric integral RF.
elliprg	Computes Carlson symmetric integral RG.
elliprj	Computes Carlson symmetric integral RJ.

Miscellaneous Functions

ellippy.misc

Miscellaneous functions related to elliptic integrals.

Functions

heuman_lambda	Computes Heuman Lambda function Λ₀(φ | m).
jacobi_zeta	Computes Jacobi Zeta function Z(φ | m).