I am trying to calculate the derivative of the Meijer's G function, Based on wolfram function identities I have found in (07.34.20.0003.01) that the derivative is expressed asl: $\frac{d}{dx}G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)=G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1-1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)+(a_1-1)G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)$
However I have found in Some handbooks such as ("Abramowitz and Stegun "Table of integrals") that a missing x should be multiplied with the left side of the identity: $x\frac{d}{dx}G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)=G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1-1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)+(a_1-1)G^{m,n}_{p,q}\left(\begin{array}{c|c}\begin{matrix}a_1,\ldots,a_p\\b_1,\ldots,b_q\end{matrix}&z\end{array}\right)$
I don't know which one is the correct identity, can we demonstrate it. Please help.