In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of
discrete orthogonal polynomials In mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure.
Examples include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk pol ...
introduced by . They are given in terms of
binomial coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...
s and the (rising)
Pochhammer symbol
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial
:\begin
(x)_n = x^\underline &= \overbrace^ \\
&= \prod_^n(x-k+1) = \prod_^(x-k) \,.
\e ...
by
:
See also
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Kravchuk polynomials
References
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*{{cite journal , first1= Xiang-Sheng , last1=Wang
, first2=Roderick , last2=Wong
, title= Global asymptotics of the Meixner polynomials
, journal = Asymptot. Anal. , year=2011 , volume=75 , number=3–4
, pages=211–231 , doi=10.3233/ASY-2011-1060
, arxiv=1101.4370
Orthogonal polynomials