Meixner polynomials

Not to be confused with Meixner–Pollaczek polynomials.

In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934). They are given in terms of binomial coefficients and the (rising) Pochhammer symbol by

$M_n(x,\beta,\gamma) = \sum_{k=0}^n (-1)^k{n \choose k}{x\choose k}k!(x-\beta)_{n-k}\gamma^{-k}$

See also

• Kravchuk polynomials