Problem 45982. Evaluate the incomplete elliptic integrals
Elliptic integrals can be used to evaluate integrals whose integrands have the form , where is a rational function in x and y and 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 .
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