elliptic integrals - again

Discussion in 'Maple' started by Michael Zedler, Jul 13, 2005.

  1. Hello,

    A few weeks ago I've had a question about integrals already - some stuff
    isn't solved yet, and apparently I can't convince Maple to help me.

    X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
    a^2/(-z^2+1+(((z-1)^2+a^2)*((z+1)^2+a^2))^(1/2));
    int(%,z=0..infinity);

    How can these things be solved?

    Kind regards,
    Michael
     
    Michael Zedler, Jul 13, 2005
    #1
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  2. sorry, I I posted the wrong stuff. It should read

    X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
    int(ln(-z^2+1+X)-ln(a^2),z=0..infinity);

    Michael
     
    Michael Zedler, Jul 13, 2005
    #2
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  3. Michael Zedler

    G. A. Edgar Guest

    X:=sqrt(((z-1)^2+a^2)*((z+1)^2+a^2));
    Y:=a^2/(-z^2+1+(((z-1)^2+a^2)*((z+1)^2+a^2))^(1/2));

    int(X,z) and int(Y,z) are elliptic integrals, Maple evaluates
    them in terms of arctan, EllipticE, EllipticF, EllipticPi.
    Sometimes with complex arguments.

    The problem of int(Y,z=0..infinity), then, is the problem of the
    limiting behavior of those functions.
     
    G. A. Edgar, Jul 13, 2005
    #3
  4. Michael Zedler

    snoofly Guest

    the answer appears to be 106

     
    snoofly, Jul 14, 2005
    #4
  5. Michael Zedler

    snoofly Guest

    sorry, scrub that - wrong calculation

     
    snoofly, Jul 14, 2005
    #5
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