Problem 45982. Evaluate the incomplete elliptic integrals

Elliptic integrals can be used to evaluate integrals whose integrands have the form R(x,sqrt(P(x))), where R(x,y) is a rational function in x and y and P(x) is a polynomial of degree 4 or less. They appear in calculations of arclength (as in Cody Problem 45979) and analysis of the motion of a pendulum.
MATLAB provides a function to compute the complete elliptic integrals of the first and second kinds but not the incomplete elliptic integrals of the first, second, and third kinds.
Write a function to evaluate the three incomplete elliptic integrals. Follow MATLAB's convention of using the parameter m, which is related to the modulus k through m = k^2.
Solve

Solution Stats

39.47% Correct | 60.53% Incorrect
Last Solution submitted on Jan 09, 2026

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers15

Suggested Problems

More from this Author319

Problem Tags

math special functions

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!