ModifiedMeijerG - Maple Help

convert/ModifiedMeijerG

convert an expression to ModifiedMeijerG form

 Calling Sequence convert( expr, ModifiedMeijerG, x )

Parameters

 expr - expression x - variable

Description

 • The convert( expr, 'ModifiedMeijerG', x ) command converts the functions in x found in expr into their equivalent ModifiedMeijerG representation, whenever possible.  Most standard special and elementary functions can be so converted, along with many complex expressions involving these.

Note: The command ModifiedMeijerG has been superseded by MeijerG.

Examples

 > $\mathrm{convert}\left(\mathrm{sin}\left(z\right),'\mathrm{ModifiedMeijerG}',z\right)$
 $\sqrt{{\mathrm{\pi }}}{}{\mathrm{ModifiedMeijerG}}{}\left(\left[\right]{,}\left[\right]{,}\left[\frac{{1}}{{2}}\right]{,}\left[{0}\right]{,}{2}{}{\mathrm{ln}}{}\left({z}\right){-}{2}{}{\mathrm{ln}}{}\left({2}\right)\right)$ (1)
 > $\mathrm{convert}\left(\mathrm{BesselK}\left(3,z\right)\mathrm{exp}\left(-az\right),'\mathrm{ModifiedMeijerG}',z\right)$
 $\frac{{\mathrm{ModifiedMeijerG}}{}\left(\left[\right]{,}\left[\right]{,}\left[{-}\frac{{3}}{{2}}{,}\frac{{3}}{{2}}\right]{,}\left[\right]{,}{2}{}{\mathrm{ln}}{}\left({z}\right){-}{2}{}{\mathrm{ln}}{}\left({2}\right)\right){}{\mathrm{ModifiedMeijerG}}{}\left(\left[\right]{,}\left[\right]{,}\left[{0}\right]{,}\left[\right]{,}{\mathrm{ln}}{}\left({z}\right){+}{\mathrm{ln}}{}\left({a}\right)\right)}{{2}}$ (2)
 > $\mathrm{convert}\left(\mathrm{hypergeom}\left(\left[1,2\right],\left[\frac{3}{2}\right],z\right),'\mathrm{ModifiedMeijerG}',z\right)$
 $\frac{\sqrt{{\mathrm{\pi }}}{}{\mathrm{ModifiedMeijerG}}{}\left(\left[{-1}{,}{0}\right]{,}\left[\right]{,}\left[{0}\right]{,}\left[{-}\frac{{1}}{{2}}\right]{,}{\mathrm{ln}}{}\left({z}\right){+}{I}{}{\mathrm{\pi }}\right)}{{2}}$ (3)

References

 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.