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::<math>\frac{U(1,b,z)}{\Gamma(b-1)}+\frac{M(1,b,z)}{\Gamma(b)}=z^{1-b}e^z</math>
::<math>M(n,b,z)</math> for non-positive integer ''n'' is a [[generalized Laguerre polynomial]].
::<math>U(n,c,z)</math> for non-positive integer ''n'' is a multiple of a generalized Laguerre polynomial, equal to <math>\frac{\Gamma(1-c)}{\Gamma(
::<math>U(c-n,c,z)</math> when ''n'' is a positive integer is a closed form with powers of ''z'', equal to <math>\frac{\Gamma(c-1)}{\Gamma(c-n)}z^{1-c}M(1-n,2-c,z)</math> when the latter exists.
::<math>U(a,a+1,z)= z^{-a}</math>
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