I am stuck in solving the following integration
$$\int_0^{\infty}y^{E-1}\cdot e^{-\frac{y}{k\cdot \sigma_{h_e}^2}}\cdot \gamma\left(R,\frac{S(y+1)-1}{k\cdot \sigma_{h_r}^2}\right)\text{d}y\tag{1}\label{integral}$$
where $E,R,k,\sigma_{h_r}^2,\sigma_{h_e}^2,S$ all are constant and $\gamma(\cdot ,\cdot)$ is the lower incomplete gamma function.
I know that \eqref{integral} is somewhat similar to equation $6.455.2$ of Table of integrals book by Gradshteyn, but not getting it properly.
Any help in this regard is highly appreciated.