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I was reading some paper on stochastic geometry when i came across this integral. I was trying to verify results myself but this one seems to be disappointing. from (d) to (c) is desirable

Although i do the instructions mentioned in footnote, i can't reach the result. my problem is reaching step (d) from (c). Here i state the problem of interest:

Prove that $$\exp \left[ -2\pi \lambda_{SI}\int_{r_{s,u}}^{\infty}\left( 1-\frac{1}{1+\left(\frac{t \times P_s \times \theta_{F_{x,u}}}{r_{x,u}^\beta}\right)^{k_{F_{x,u}}}} \right)r_{x,u}dr_{x,u}\right] = \, \, \quad \exp\left[ -\pi \lambda_{SI} r_{s,u}^2 (\,_2F_1[k_{F_{x,u}},-\frac{2}{\beta},1-\frac{2}{\beta},-\frac{t P_s \theta_{F_{x,u}}}{r_{x,u}^\beta}]-1) \right]$$

Any way of proving is appreciated. Thanks in advance.

Also $\,_pF_q[a,b,c,z]$ is the hyper geometric function: https://en.wikipedia.org/wiki/Hypergeometric_function

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