Tricomi–Carlitz polynomials

In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–) Karlin–McGregor polynomials are polynomials studied by Tricomi (1951),^[1] Carlitz (1958),^[2] and Karlin and McGregor (1959),^[3] related to random walks on the positive integers.

They are given in terms of Laguerre polynomials by

${\displaystyle \ell _{n}(x)=(-1)^{n}L_{n}^{(x-n)}(x).}$

They are special cases of the Chihara–Ismail polynomials.