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I'm not too sure my question is suitable here, but I did not have any luck at math.stackexchange (http://math.stackexchange.com/questions/234989/int-infty-0xr-s-11-x-s1-x2-fracrm2dx) so I thought I'd try and see if I can get some help here.

I'm not too sure my question is suitable here, but I did not have any luck at math.stackexchange (https://math.stackexchange.com/questions/234989/int-infty-0xr-s-11-x-s1-x2-fracrm2dx) so I thought I'd try and see if I can get some help here.

$\frac{\Gamma(r(m-1))\Gamma(s-r(m-1))}{\Gamma(s)}$$_{3}F_{2}\left( \frac {mr}{2},\frac{r(m-1)}{2},\frac{1+r(m-1)}{2};\frac{1-s+r(m-1)}{2},1+\frac {s-r(m+1)}{2};-1\right)$ $ -\frac{s\Gamma\left(\frac{r(m-1)-1-s}{2}\right)\Gamma\left( \frac{1+r+s}{2}\right) } {2\Gamma(\frac{mr}{2})}$$_{3}F_{2}\left( \frac{1+s}{2},1+\frac{s}{2} ,\frac{1+r+s}{2};\frac{3}{2},\frac{3+s-r(m-1)}{2};-1\right)$ $ +\Gamma\left( \frac{r(m-1)-s}{2}\right) \Gamma\left( \frac{r+s} {2}\right)$$_{3}F_{2}\left( \frac{1+s}{2},\frac{r+s}{2},\frac{s}{2} ;\frac{1}{2},1+\frac{s-r(m-1)}{2};-1\right)$

$\frac{\Gamma(r(m-1))\Gamma(s-r(m-1))}{\Gamma(s)}{}_3 F_2\left( \frac {mr}{2},\frac{r(m-1)}{2},\frac{1+r(m-1)}{2};\frac{1-s+r(m-1)}{2},1+\frac {s-r(m+1)}{2};-1\right)$ $ -\frac{s\Gamma\left(\frac{r(m-1)-1-s}{2}\right)\Gamma\left( \frac{1+r+s}{2}\right) } {2\Gamma(\frac{mr}{2})}{}_3 F_2\left( \frac{1+s}{2},1+\frac{s}{2} ,\frac{1+r+s}{2};\frac{3}{2},\frac{3+s-r(m-1)}{2};-1\right)$ $ +\Gamma\left( \frac{r(m-1)-s}{2}\right) \Gamma\left( \frac{r+s} {2}\right){}_3 F_2\left( \frac{1+s}{2},\frac{r+s}{2},\frac{s}{2} ;\frac{1}{2},1+\frac{s-r(m-1)}{2};-1\right)$