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Math Help - Integration with hypergeometric function

  1. #1
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    Integration with hypergeometric function

    How to integrate:

    _{2}F_{1}(B;C;D;Ex^{2})\,Ax

    where _{2}F_{1}(...) is the hypergeometric function, x is the independent variable and A, B, C, D, and E are constants.
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  2. #2
    MHF Contributor
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    Re: Integration with hypergeometric function

    Quote Originally Posted by JulieK View Post
    How to integrate:

    _{2}F_{1}(B;C;D;Ex^{2})\,Ax

    where _{2}F_{1}(...) is the hypergeometric function, x is the independent variable and A, B, C, D, and E are constants.
    make the sub

    $u=e x^2$

    $du=2ex~dx$

    and find

    $\dfrac a {2e} \displaystyle{\int} _2F_1(b,c,d,u) ~du=\dfrac a {2e} \frac{\Gamma (d) \left(\Gamma (d-1) \, _2\tilde{F}_1(b-1,c-1;d-1;u)-1\right)}{(b-1) (c-1) \Gamma (d-1)}$

    $_2\tilde{F}_1(b,c,d,u)$ is the http://reference.wolfram.com/mathema...gularized.html
    Last edited by romsek; June 29th 2014 at 02:08 PM.
    Thanks from topsquark and JulieK
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