Meixner polynomials

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

${\displaystyle M_{n}(x,\beta ,\gamma )=\sum _{k=0}^{n}(-1)^{k}{n \choose k}{x \choose k}k!(x+\beta )_{n-k}\gamma ^{-k}}$.

Meixner polynomials belong to the Hahn class of polynomials, along with Hahn polynomials, Charlier polynomials, and Kravchuk polynomials.

See also

• Kravchuk polynomials

Notes

References

This polynomial-related article is a stub. You can help Wikipedia by adding missing information.

• v
• t
• e