Angelescu polynomials

In mathematics, the Angelescu polynomials π_n(x) are a series of polynomials generalizing the Laguerre polynomials introduced by Aurel Angelescu. The polynomials can be given by the generating function$${\displaystyle \phi \left({\frac {t}{1-t}}\right)\exp \left(-{\frac {xt}{1-t}}\right)=\sum _{n=0}^{\infty }\pi _{n}(x)t^{n}.}$$^[1][2]

They can also be defined by the equation $${\displaystyle \pi _{n}(x):=e^{x}D^{n}[e^{-x}A_{n}(x)],}$$where ${\displaystyle {\frac {A_{n}(x)}{n!}}}$ is an Appell set of polynomials^[which?].^[3]