The equation I want to derive is $$\exp\left\{-2\pi\lambda\int^{\infty}_r\left(1-\frac{1}{1+zPv^{-\alpha}}\right)vdv\right\}=\exp\left\{-\pi\lambda^2\left[{}_2F_1\left(-\frac{2}{\alpha},1;1-\frac{2}{\alpha},-\frac{zP}{r^{\alpha}}\right)-1\right]\right\}$$ I was trying to use the formula below after some manipulates about changing of variables $$B(b,c-b)\,_2F_1(a,b;c;z) = \int_0^1 x^{b-1} (1-x)^{c-b-1}(1-zx)^{-a} \, dx$$ where $B$ is the Beta function. But I did not get the results. Any help? Thanks!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.