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Elliptic integrals

  1. Aug 24, 2008 #1
    and the integral goes over [0,1]

    The book I'm reading says this is an elliptic integral, meaning that it is the integral of a rational function of x and y in which y² is a polynomial in x, of degree 3 or 4, having simple roots.

    What does the author possibly mean?

    What y? Why y² polynomial in x? Why degree 3 0r 4? And yes, why having simple roots?

    Could someone give some hints?

    thank you
  2. jcsd
  3. Aug 24, 2008 #2


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    Actually, I am not familiar with that definition! An "elliptic integral" is a generalization of the kind of integral you get trying to calculate the circumference of an ellipse. In any case, here if you take y2 to be 1- x4, a fourth dergee polynomial with obviously simple roots, then [itex](1- x^4)^{-1/2}= \frac{1}{\sqrt{1- x^4}}= \frac{1}{\sqrt{y^2}}= \frac{1}{y}[/itex]. a rational function of y.
  4. Aug 24, 2008 #3


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  5. Aug 25, 2008 #4
    many thanks!
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