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I am looking for a way to solve this Integral:

$$ \int_{x=0.5}^\infty \int_{t=0}^\infty \left[ Q(\sqrt{(S \times t)}) \times (x+0.5)^{n-k-1} \times (x-0.5)^{k-1} \times x^n \times t^{n-1} \times e^{-4tx^2} \right] dt dx $$ where
$$ Q(y) = \int_{z=y}^\infty {e^{-z^2/2} \over \sqrt{2\pi}} dz, $$ $$ k \in \mathbb{Z}, \mbox{ }k \ge 1,$$ $$ n \in \mathbb{Z}, \mbox{ }n \ge 2, \mbox{ }n \ge k,$$ $$S \ge 0.$$

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This is a definite integral. You can use Mathematica to numerically integrate, and assuming that the integrand is not highly oscillatory, which it appears not to be, you can obtain a value accurate to arbitrarily high accuracy. –  Christopher A. Wong May 31 '13 at 10:08
    
Christopher A. Wong: I used Mathematica software (Integrate[] command). But unfortunately it can't solve it! –  M Mashreghi May 31 '13 at 12:48
1  
Try NIntegrate. You also can try other mathematical software. –  Christopher A. Wong May 31 '13 at 19:07
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