convert/GAMMA_related converts, when possible, the special functions in an expression into GAMMA_related functions. The GAMMA_related transcendental functions are

FunctionAdvisor( GAMMA_related );

The 8 functions in the "GAMMA_related" class are:

$\left[\mathrm{{\rm B}}\,\mathrm{\Gamma }\,\mathrm{binomial}\,\mathrm{doublefactorial}\,\mathrm{factorial}\,\mathrm{lnGAMMA}\,\mathrm{multinomial}\,\mathrm{pochhammer}\right]$

$\mathrm{WhittakerW}\left(-\frac{1}{2}+\frac{1}{2}a\,\frac{1}{2}a\,z\right)z^a\mathrm{hypergeom}\left(\left[a\right]\,\left[1+a\right]\,-z\right)$

$\mathrm{WhittakerW}\left(-\frac{1}{2}+\frac{a}{2}\,\frac{a}{2}\,z\right)z^a\mathrm{hypergeom}\left(\left[a\right]\,\left[1+a\right]\,-z\right)$

$\mathrm{convert}\left(\,\mathrm{GAMMA\_related}\right)$

$\frac{\mathrm{\Gamma }\left(a\,z\right){\ⅇ}^{\frac{z}{2}}a\mathrm{\Gamma }\left(a\right)}{z^{-\frac{1}{2}+\frac{a}{2}}}-\frac{{\mathrm{\Gamma }\left(a\,z\right)}^2{\ⅇ}^{\frac{z}{2}}a}{z^{-\frac{1}{2}+\frac{a}{2}}}$

$\frac{z^a}{\exp \left(z\right)}\mathrm{KummerU}\left(1\,a+1\,z\right)+z\mathrm{hypergeom}\left(\left[1\,1\,1\,1\right]\,\left[2\,2\,2\right]\,z\right)$

$\frac{z^a\mathrm{KummerU}\left(1\,1+a\,z\right)}{{\ⅇ}^z}+z\mathrm{hypergeom}\left(\left[1\,1\,1\,1\right]\,\left[2\,2\,2\right]\,z\right)$

$\mathrm{convert}\left(\,\mathrm{GAMMA\_related}\right)$

$\mathrm{\Gamma }\left(a\,z\right)+z\mathrm{hypergeom}\left(\left[1\,1\,1\,1\right]\,\left[2\,2\,2\right]\,z\right)$

$\mathrm{LaguerreL}\left(-a\,a\,-z\right)$

$\mathrm{LaguerreL}\left(-a\,a\,-z\right)$

$\mathrm{convert}\left(\,\mathrm{GAMMA\_related}\right)$

$-\frac{\left(\left\{\begin{array}{cc}1& -a=0\\ \frac{\sin \left(\mathrm{\pi }a\right)}{\mathrm{\pi }a}& \mathrm{otherwise}\end{array}\right.\right)a\mathrm{\Gamma }\left(a\,z\right)}{z^a}+\frac{\left(\left\{\begin{array}{cc}1& -a=0\\ \frac{\sin \left(\mathrm{\pi }a\right)}{\mathrm{\pi }a}& \mathrm{otherwise}\end{array}\right.\right)a\mathrm{\Gamma }\left(a\right)}{z^a}$