ellippy

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.

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

Features

Legendre's complete integrals
- ellipk: Complete elliptic integral of the first kind (K).
- ellipe: Complete elliptic integral of the second kind (E).
- ellippi: Complete elliptic integral of the third kind (Π).
- ellipd: Complete elliptic integral of Legendre's type (D).
Legendre's incomplete integrals
- ellipf: Incomplete elliptic integral of the first kind (F).
- ellipeinc: Incomplete elliptic integral of the second kind (E).
- ellippiinc: Incomplete elliptic integral of the third kind (Π).
- ellipdinc: Incomplete elliptic integral of Legendre's type (D).
Bulirsch's integrals
- cel: General complete elliptic integral in Bulirsch's form.
- cel1: Complete elliptic integral of the first kind in Bulirsch's form.
- cel2: Complete elliptic integral of the second kind in Bulirsch's form.
- el1: Incomplete elliptic integral of the first kind in Bulirsch's form.
- el2: Incomplete elliptic integral of the second kind in Bulirsch's form.
- el3: Incomplete elliptic integral of the third kind in Bulirsch's form.
Carlson's symmetric integrals
- elliprf: Symmetric elliptic integral of the first kind (RF).
- elliprg: Symmetric elliptic integral of the second kind (RG).
- elliprj: Symmetric elliptic integral of the third kind (RJ).
- elliprc: Degenerate elliptic integral of RF (RC).
- elliprd: Degenerate elliptic integral of the third kind (RD).
Miscellaneous functions
- jacobi_zeta: Jacobi Zeta function (Z).
- heuman_lambda: Heuman Lambda function (Λ0).

Citation

EllipPy is based on a Rust library, Ellip. The paper is published in the Journal of Open Source Software. If EllipPy is helpful to your work, please consider citing Ellip:

Pornsiriprasert, S., (2026). Ellip: An Elliptic Integral Library for Rust. Journal of Open Source Software, 11(118), 9386, https://doi.org/10.21105/joss.09386

Bibtex format:

@article{Pornsiriprasert2026,
    doi = {10.21105/joss.09386}, 
    url = {https://doi.org/10.21105/joss.09386}, 
    year = {2026}, 
    publisher = {The Open Journal}, 
    volume = {11}, number = {118}, pages = {9386},
    author = {Pornsiriprasert, Sira}, 
    title = {Ellip: An Elliptic Integral Library for Rust}, 
    journal = {Journal of Open Source Software} }

License
- OSI Approved :: BSD License
Operating System
- OS Independent
Programming Language
- Python :: 3

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BLAKE2b-256	`f521b743e26c2c96e3c21e04b2bb595eb56ceadd5ae2d97df04cafbc0c843017`

Algorithm	Hash digest
SHA256	`d065c1dafa5da7445b588d867161fa5b6ad7a40225ca10edfc7f0e156d18bf94`
MD5	`26ae2b125cab5c4931d7c10663ce58ff`
BLAKE2b-256	`71a877daa8df176b76e7e6a19c3932dc66542c799fc0752b520751cdd43dbfa6`

Algorithm	Hash digest
SHA256	`f2e0da64b3203b876c90d897ffaf4d274775a7939aadb8ceaed4c5625adf7076`
MD5	`af94935b530a3e3600995e5b2559b301`
BLAKE2b-256	`095e28f27ed805e3c39bbff418f0e6cc22f5d043d243285cc216ea56be701f08`

Algorithm	Hash digest
SHA256	`8e47907fa7391d7d9a7be489ddf0d9f674b6086d94276c50015dc2856772cfc8`
MD5	`2ae8fa7cc012990eb8e7678d4a4fefc4`
BLAKE2b-256	`4299e665cf070e65310e717c07f53b8a5e512efaaefd9471b644c69ed25897cd`

ellippy 1.1.1

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1 maintainer

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Algorithm	Hash digest
SHA256	`089496d91c741314b23fd6e3a1c7074d5f94d5f4b3f9a76f14db636f98afb4d6`
MD5	`965ef37458d475a0150bcd9e3419589b`
BLAKE2b-256	`907e3606a91edc3cf49793f3fc1a5d16ad4b0e5c07d17a55b8eec32da04478d6`

Algorithm	Hash digest
SHA256	`44b5fcd2bd0d6614541791149c70d596e1e308c169843f51d46b33e9edd1f31b`
MD5	`20e108d9b4c8248c237a968523a47a4b`
BLAKE2b-256	`e492d718a9dcd65543521c7c1ae5d8794d50ef13e2e108cd9558a43704e1e91d`

Algorithm	Hash digest
SHA256	`2d5b06ad4e439dc48c4df445d4cd768c8847ec3d61eec6ebe68a8cc824225658`
MD5	`cefb28a733007c438e3fcefcc2ceac6b`
BLAKE2b-256	`7d22854d4d44b0f3c09f136e0da668068b28b7baf99fdeca84597e66cc71770f`

Algorithm	Hash digest
SHA256	`45ea5dc37baa74bd0a0ee2dbe15f64aea80cab5daa6995ddee243045d6873b95`
MD5	`4a7aad22d05b031dc80231fa114b1b94`
BLAKE2b-256	`62a80f89d83a7459bbddf0c52b5d2f9f17639cf5f02905b0be6336d269f7caed`

Algorithm	Hash digest
SHA256	`aa670af5c11aeeb42ecd3fdd54fa589b92f0f922bd06714cefe6e6ac60a63580`
MD5	`c35ac2481309049c2df3502c63015249`
BLAKE2b-256	`9aae442552d8416b48c73c00728e0c56805c128006dde5b90e876cd11412bb5c`

Algorithm	Hash digest
SHA256	`f483faf7850d3fcecc1544d1ef925bc2b34f855821b7dcb5125e6dabb947520e`
MD5	`d4b7b396e56f2fc7900c497657f135fe`
BLAKE2b-256	`933101cf07d030694f9ffa31ce234c2490c3791ef0e3049c2c1e2f55ad1f3060`

Algorithm	Hash digest
SHA256	`28047282c2feaef463250d86454a0bcaee5cfb4c8ffcd6bc4d8eafeb7878d773`
MD5	`f2cec9c1ed83a497f2550b5ffdf24493`
BLAKE2b-256	`7a0b9dab421888a8a1e3862cc51a26080283efcea1a1bb29402872bf6fe7bc64`

Algorithm	Hash digest
SHA256	`97bb6fa5a092bd425b20fda196c99eb899f5b022ff375e529930ba5d1a13242f`
MD5	`2dea7d3d1addf8d13cdbaf3500674df6`
BLAKE2b-256	`9acdb34d371b40f600fcf12a1974ff811248c222fb993308244560fc7111db18`

Algorithm	Hash digest
SHA256	`020501b658c4c04a61d75f89f3d068fba426b4e1259ea4d0ba95071e88476892`
MD5	`a6d48e106ab4878d956c5da550372df7`
BLAKE2b-256	`c07b1c012bf339c2151d528a6189b44f61515bb73e52505204e0ab431a4f7b56`

Algorithm	Hash digest
SHA256	`17a43c758bbd8f753c089b4a8325113ff79497409826a24ff0cfd930ebd07ce9`
MD5	`4dffb6f5b44230597e6638ddea7766eb`
BLAKE2b-256	`ff41c3b6db115d0f8e0f48ed090a0340eb81cbfd5963ce203914bf6c0a626907`