# Definite integral $\int_{y}^{\infty}$ involving two Meijer's G function

I want to evalute one of these integrals: $$\begin{equation}I = \int_{y}^{\infty} \large{G}_{2,2}^{1,2}\left( x \left| \begin{array}{cc} 1,1 \\ 1,0 \end{array} \right. \right) \large{G}_{1,3}^{3,0}\left( \omega x \left| \begin{array}{cc} \phi \\ \phi -1,\alpha -1,\beta -1 \end{array} \right. \right)dx \end{equation}$$ or $$\begin{equation}I = \int_{y}^{\infty}x^{-1} \large{G}_{2,2}^{1,2}\left( x \left| \begin{array}{cc} 1,1 \\ 1,0 \end{array} \right. \right) \large{G}_{1,3}^{3,0}\left( \omega x^\frac{l}{k} \left| \begin{array}{cc} \phi +1 \\ \phi ,\alpha ,\beta \end{array} \right. \right)dx \end{equation}$$ where $\omega$ ,$\phi$ ,$\alpha$ ,$\beta$ ,$\mathcal l$ and $\mathcal k$ are non-zero positive constants

I serached for a formula that involving two meijer's G functions and I found only 07.34.21.0013.01 http://functions.wolfram.com/07.34.21.0013.01

but for integral $\int_{0}^{\infty}$ , so any references or ideas to evaluate the integrals will be helpful