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Math Help - elliptic integral

  1. #1
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    elliptic integral

    Hi,

    how to transform the following integral to elliptic integral of the second kind:

    int 0_pi/2 (1-(k*sin(phi))^2)^-(3/2)

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  2. #2
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    Re: elliptic integral

    Hi !
    It's a complete elliptic integral of the third kind, in a particular case with a well-known relationship to the complete elliptic integral of the first kind.
    Attached Thumbnails Attached Thumbnails elliptic integral-elliptic-integral.jpg  
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  3. #3
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    Re: elliptic integral

    Thanks JJacquelin

    would you please tell me how to find the prove of the relation between the elliptic integrals of second and third kind?
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  4. #4
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    Re: elliptic integral

    Quote Originally Posted by mopen80 View Post
    would you please tell me how to find the prove of the relation between the elliptic integrals of second and third kind?
    The relation between the elliptic integrals of second and third kind is much more complicaded (attachment)
    This results from arduous work done centuries ago, when the special fuctions such as elliptic integral where in fashion.
    Attached Thumbnails Attached Thumbnails elliptic integral-relationship.jpg  
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