I'm trying to understand how a Meijer G function changes in parameters when I change the function a little bit. For example, I know that the meijer G parameters of the following functions \begin{aligned} \cos x=\sqrt{\pi} G_{0,2}^{1,0}\left(\begin{array}{c|c} - & x^2 \\ 0, \frac{1}{2} & \frac{-\pi}{4} \end{array}\right), \quad \forall x \end{aligned}
\begin{aligned} \sin x=\sqrt{\pi} G_{0,2}^{1,0}\left(\begin{array}{c|c} - & x^2 \\ \frac{1}{2}, 0 & \frac{-\pi}{4} \end{array}\right), \quad -\frac\pi2\leq \arg x \leq \frac\pi2 \end{aligned}
But I want to be able to ask like what is the meijer G parameters function of $\sin(x) + \cos(x)$ (and other simple combinations of elementary functions as well. Does anyone know a good lookup table or software that will allow me to do that?