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Approximating Elliptic Integrals on the computer

  1. Dec 8, 2006 #1
    1. The problem statement, all variables and given/known data

    Express (EllipticK(x)/EllipticE(x)-1) to two terms with a taylor series

    2. Relevant equations

    EllipticE(x) = Int((1-k^2*_alpha1^2)^(1/2)/(1-_alpha1^2)^(1/2),_alpha1 = 0 .. 1), `with no restrictions on `(x)

    EllipticK(k) = Int(1/((1-_alpha1^2)^(1/2)*(1-k^2*_alpha1^2)^(1/2)),_alpha1 = 0 .. 1)

    Note this is the maple code expression for these

    3. The attempt at a solution

    Using Maple (canadian mathematica) I got -x-5/4*x^3

    I mainly want to verify this to make sure I'm solving a particular DE correctly.
  2. jcsd
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