Table 1 The effect of the Erdélyi-Kober operators on the Meijer's $G_{p,q+1}^{1,p}$-functions

$I_{1,1}^{a_2-1,b_1-a_2}$

$\begin{array}{l}{G}_{1,1}^{1,1}\to G_{2,2}^{1,2}\left[{}_{0,1-b_1}^{1-a_1,1-a_2}|-z\right]\\ (b_1>a_2)\end{array}$

$D_{1,1}^{b_1-1,a_2-b_1}$

$G_{1,1}^{1,1}\to G_{2,2}^{1,2}\left(b_1<a_2\right)$

$I_{1,1}^{a_2-1,b_2-a_2}\left(b_2>a_2\right)$

$G_{1,2}^{1,1}\to G_{2,3}^{1,2}\left[{}_{0,1-b_1,1-b_2}^{1-a_1,1-a_2}|-z\right]$

$D_{1,1}^{b_2-1,a_2-b_2}\left(b_2<a_2\right)$

$G_{1,2}^{1,1}\to G_{2,3}^{1,2}$

$I_{1,1}^{a_1-1,b_2-a_1}\left(b_2>a_1\right)$

$G_{0,2}^{1,0}\to G_{1,3}^{1,1}\left[{}_{0,1-b_1,1-b_2}^{1-a_1}|-z\right]$

$D_{1,1}^{b_2-1,a_1-b_2}\left(b_2<a_1\right)$

$G_{0,2}^{1,0}\to G_{1,3}^{1,1}$