convert MeijerG/hypergeom to standard special and elementary functions - Maple Help

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convert/StandardFunctions - convert MeijerG/hypergeom to standard special and elementary functions

 Calling Sequence convert( $\mathrm{expr}$, StandardFunctions )

Parameters

 expr - expression

Description

 • The convert( expr, StandardFunctions ) command converts functions that are represented in terms of MeijerG or hypergeom functions into the standard special and elementary functions found in such texts as Handbook of Mathematical Functions by Abramowitz and Stegun, and Integrals and Series, Volume 3: More Special Functions by A.P. Prudnikov, Yu. Brychkov, and O. Marichev. Examples of these standard functions include Bessel and Legendre functions, elliptic integrals, etc.

Examples

 > $\mathrm{convert}\left(\mathrm{hypergeom}\left(\left[1,2\right],\left[\frac{3}{2}\right],z\right),\mathrm{StandardFunctions}\right)$
 ${-}\frac{{1}}{{2}{}{z}{-}{2}}{+}\frac{{1}}{{2}}{}\frac{\sqrt{{-}{z}{+}{1}}{}{\mathrm{arcsin}}{}\left(\sqrt{{z}}\right)}{{\left({z}{-}{1}\right)}^{{2}}{}\sqrt{{z}}}$ (1)
 > $\mathrm{convert}\left(\mathrm{MeijerG}\left(\left[\left[\right],\left[\right]\right],\left[\left[0\right],\left[0\right]\right],\frac{{z}^{2}}{4}\right),\mathrm{StandardFunctions}\right)$
 ${\mathrm{BesselJ}}{}\left({0}{,}{z}\right)$ (2)
 > $\mathrm{assume}\left(n,\mathrm{nonnegint}\right)$
 > $\mathrm{convert}\left(\mathrm{hypergeom}\left(\left[-n,-n\right],\left[\frac{1}{2}-2n\right],z\right),\mathrm{StandardFunctions}\right)$
 $\frac{{\left({-}{1}\right)}^{{\mathrm{n~}}}{}{\left({2}{}{\mathrm{n~}}\right){!}}^{{2}}{}{\left({4}{}{z}\right)}^{{\mathrm{n~}}}{}{\mathrm{LegendreP}}{}\left({2}{}{\mathrm{n~}}{,}\sqrt{\frac{{z}{-}{1}}{{z}}}\right)}{\left({4}{}{\mathrm{n~}}\right){!}}$ (3)