convert/Kummer converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Kummer functions. The Kummer functions are

FunctionAdvisor( Kummer );

The 2 functions in the "Kummer" class are:

$\left[\mathrm{KummerM}\,\mathrm{KummerU}\right]$

$\mathrm{AiryAi}\left(z\right)$

$\mathrm{AiryAi}\left(z\right)$

$\mathrm{convert}\left(\,\mathrm{Kummer}\right)$

$\frac{\frac{3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\mathrm{KummerM}\left(\frac{1}{6}\,\frac{1}{3}\,\frac{4z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{3}\right)}{3\mathrm{\Gamma }\left(\frac{2}{3}\right)}-\frac{z{3}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}\mathrm{\Gamma }\left(\frac{2}{3}\right)\mathrm{KummerM}\left(\frac{5}{6}\,\frac{5}{3}\,\frac{4z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{3}\right)}{2\mathrm{\pi }}}{{\ⅇ}^{\frac{2z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{3}}}$

$\mathrm{HermiteH}\left(a\,z\right)\mathrm{LaguerreL}\left(2\,\exp \left(z\right)\right)$

$\mathrm{HermiteH}\left(a\,z\right)\mathrm{LaguerreL}\left(2\,{\ⅇ}^z\right)$

$\mathrm{convert}\left(\&comma;\mathrm{Kummer}\right)\mathbf{assuming}0<\mathrm{\Re }\left(z\right)$

$2^a\sqrt{\mathrm{\pi }}\left(\frac{\mathrm{KummerM}\left(-\frac{a}{2}\&comma;\frac{1}{2}\&comma;z^2\right)}{\mathrm{\Gamma }\left(\frac{1}{2}-\frac{a}{2}\right)}-\frac{2z\mathrm{KummerM}\left(\frac{1}{2}-\frac{a}{2}\&comma;\frac{3}{2}\&comma;z^2\right)}{\mathrm{\Gamma }\left(-\frac{a}{2}\right)}\right)\mathrm{KummerM}\left(\mathrm{-2}\&comma;1\&comma;\mathrm{KummerM}\left(1\&comma;1\&comma;z\right)\right)$

$\frac{\left(\exp \left(z\right)\mathrm{erf}\left(z^2\right)+\mathrm{WhittakerW}\left(-1\&comma;\frac{1}{2}\&comma;z\right)\exp \left(\frac{1}{2}z\right)\right)\mathrm{MeijerG}\left(\left[\left[1-a\right]\&comma;\left[\right]\right]\&comma;\left[\left[0\&comma;1-b\right]\&comma;\left[\right]\right]\&comma;\frac{1}{z}\right)}{\mathrm{BesselK}\left(-3\&comma;1-z\right)}$

$\frac{\left({\&ExponentialE;}^z\mathrm{erf}\left(z^2\right)+\mathrm{WhittakerW}\left(\mathrm{-1}\&comma;\frac{1}{2}\&comma;z\right){\&ExponentialE;}^{\frac{z}{2}}\right)\mathrm{MeijerG}\left(\left[\left[1-a\right]\&comma;\left[\right]\right]\&comma;\left[\left[0\&comma;1-b\right]\&comma;\left[\right]\right]\&comma;\frac{1}{z}\right)}{\mathrm{BesselK}\left(3\&comma;1-z\right)}$

$\mathrm{convert}\left(\&comma;\mathrm{Kummer}\right)$

$\frac{\left(\frac{2\mathrm{KummerM}\left(1\&comma;1\&comma;z\right)z^2\mathrm{KummerM}\left(\frac{1}{2}\&comma;\frac{3}{2}\&comma;-z^4\right)}{\sqrt{\mathrm{\pi }}}+\frac{\mathrm{KummerU}\left(2\&comma;2\&comma;z\right)z\mathrm{KummerM}\left(1\&comma;1\&comma;\frac{z}{2}\right)}{{\&ExponentialE;}^{\frac{z}{2}}}\right)\left(\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }\left(1-b\right)\mathrm{KummerM}\left(a\&comma;b\&comma;\frac{1}{z}\right)+\frac{\mathrm{KummerM}\left(1+a-b\&comma;2-b\&comma;\frac{1}{z}\right)\mathrm{\Gamma }\left(1+a-b\right)\mathrm{\Gamma }\left(-1+b\right)}{{\left(\frac{1}{z}\right)}^{-1+b}}\right)}{8\sqrt{\mathrm{\pi }}{\left(1-z\right)}^3\mathrm{KummerU}\left(\frac{7}{2}\&comma;7\&comma;2-2z\right){\&ExponentialE;}^{-1+z}}$