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The convert( expr, 'MeijerG') command converts the functions found in expr into their equivalent MeijerG representation, whenever possible. Most special and all elementary functions can be so converted.

$\mathrm{BesselK}\left(n\,z\right)\:$

$\mathrm{BesselK}\left(n\,z\right)=\mathrm{convert}\left(\mathrm{BesselK}\left(n\,z\right)\,\mathrm{MeijerG}\right)$

$\mathrm{BesselK}\left(n\,z\right)=\frac{\mathrm{MeijerG}\left(\left[\left[\right]\,\left[\right]\right]\,\left[\left[\frac{n}{2}\,-\frac{n}{2}\right]\,\left[\right]\right]\,\frac{z^2}{4}\right)}{2}$

$\mathrm{hypergeom}\left(\left[a\,b\right]\,\left[c\right]\,z\right)\:$

$\mathrm{hypergeom}\left(\left[a\,b\right]\,\left[c\right]\,z\right)=\mathrm{convert}\left(\mathrm{hypergeom}\left(\left[a\,b\right]\,\left[c\right]\,z\right)\,\mathrm{MeijerG}\right)$

$\mathrm{hypergeom}\left(\left[a\,b\right]\,\left[c\right]\,z\right)=\frac{\mathrm{\Gamma }\left(c\right)\mathrm{MeijerG}\left(\left[\left[1-a\,1-b\right]\,\left[\right]\right]\,\left[\left[0\right]\,\left[1-c\right]\right]\,-z\right)}{\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }\left(b\right)}$

$\mathrm{convert}\left(\sin \left(z\right)\,\mathrm{MeijerG}\right)$

$\sin \left(z\right)$

$\sin \left(z\right)\:$

$\sin \left(z\right)=\mathrm{convert}\left(\sin \left(z\right)\,\mathrm{MeijerG}\,\mathrm{include}=\mathrm{all}\right)$

$\sin \left(z\right)=\sqrt{\mathrm{\pi }}\mathrm{MeijerG}\left(\left[\left[\right]\,\left[\right]\right]\,\left[\left[\frac{1}{2}\right]\,\left[0\right]\right]\,\frac{z^2}{4}\right)$

Prudnikov, A.P.; Brychkov, Yu; and Marichev, O. Integrals and Series. Gordon and Breach Science, 1990. Vol. 3: More Special Functions.

Roach, K. "Meijer G Function Representations." In Proceedings of ISSAC '97, pp. 205-211. Edited by Wolfgang Kuchlin. New York: ACM Press, 1997.