In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–)Karlin–McGregor polynomials are polynomials studied by and and , related to
random walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space.
An elementary example of a rand ...
s on the
positive integers
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positiv ...
.
They are given in terms of
Laguerre polynomials by
:
They are special cases of the
Chihara–Ismail polynomials.
References
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Orthogonal polynomials
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