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{{distinguish|Meixner–Pollaczek polynomials}}
In mathematics, '''Meixner polynomials''' (also called '''discrete Laguerre polynomials''') are a family of [[discrete orthogonal polynomials]] introduced by {{harvs|txt|authorlink=Josef Meixner|first=Josef|last= Meixner|year=1934}}. They are given in terms of binomial coefficients and the (rising) [[Pochhammer symbol]] by
:<math>M_n(x,\beta,\gamma) = \sum_{k=0}^n (-1)^k{n \choose k}{x\choose k}k!(x-\beta)_{n-k}\gamma^{-k}</math>

==See also==
*[[Kravchuk polynomials]]

==References==
*{{cite journal| last1=Meixner | first1=J. | title=Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion   | doi=10.1112/jlms/s1-9.1.6  | year=1934  | journal=Journal of the London Mathematical Society | volume=s1-9 | pages=6–13}}
*{{cite journal | first1=W. A. | last1=Al-Salam
|title=On a characterization of Meixner's Polynomials
|journal=Quart. J. Math. | year=1966 | volume=17 | number=1 | pages=7-10
|doi=10.1093/qmath/17.1.7 
}}
*{{cite journal| first1=N. M. |last1=Atakishiyev | first2=S. K. | last2=Suslov
|title=The Hahn and Meixner polynomials of an imaginary argument and some of their applications
|year=1985 | journal= J. Phys. A: Math. Gen.
|doi=10.1088/0305-4470/18/10/014 |volume=18 | number=10 | pages=1583
}}
*{{cite journal| first1= G. E. | last1=Andrews | first2=Richard | last2=Askey
|title=Classical orthogonal polynomials
|year=1985 | journal = Lect. Notes Math. | volume=1171 | pages = 36-82
|doi=10.1007/BFb0076530
}}
*{{cite journal | first1= M. V. | last1=Tratnik
|title=Multivariable Meixer, Krawtchouk, and Meixner-Pollaczek polynomials
|year=1989 | journal= J. Math. Phys. | volume=30 | number=12 | pages=2740 | doi=10.1063/1.528507 
}}
*{{cite journal | first1= M. V. | last1=Tratnik
|title=Some multivariable orthogonal polynomials of the Askey tableau-discrete families
|journal = J. Math. Phys. | year=1991 | volume=32 | number=9
|pages=2337 | doi=10.1063/1.529158 
}}
*{{cite journal | first1=H. | last1=Bavinck | first2=H. | last2=Vanhaeringen
|title=Difference equtions for generalized Meixner Polynomials
|journal= J. Math. Anal. Applic. | year=1994 | volume=184 | number=3
|doi=10.1006/jmaa.1994.1214 | pages=453-463
}}
*{{cite journal | first1= X.-S. | last1=Jin | first2=R. |last2=Wong
|title= Uniform asymptotic expansion for Meixner polynomials
|year=1998 | volume=14 | number=1 | pages=113-150
|journal=Construct. Approx. | doi=10.1007/s003659900066
}}
*{{cite journal | first1=Maria |last1=&Aacute;lvarez de Morales | first2=T. E. | last2=P&eacute;rez
|first3=M. A. | last3=Pi&ntilde;ar | first4=A. | last4=Ronveaux
|title=Non-standard orthogonality for Meixner Polynomials
|year=1999 | journal = El. Trans. Num. Anal. | volume=9 | pages=1-25
|url=http://www.emis.ams.org/journals/ETNA/vol.9.1999/pp1-25.dir/pp1-25.pdf
}}
*{{cite journal| first1=X.-S. | last1=Jin | first2=R. | last2=Wong
|title=Asymptotic formulas for the zeros of Meixner Polynomials
|journal= J. Approx. Theory | year=1999 | volume=96 | number=2 | pages=281-300
|doi=10.1006/jath.1998.3235
}}
*{{cite arxiv| eprint=math/0609806 | first1=Alexei | last1=Borodin
|first2=Grigori |last1=Olshanski | title=Meixner polynomials and random partitions |year=2006
}}
*{{dlmf|id=18.19|title=Hahn Class: Definitions|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}
*{{cite journal | first1=L. |last1=Boelen | first2=Galina | last2=Filipuk
|first3=Walter | last3= Van Assche | journal=J. Phys. A: Math. Theor.
|title=Recurrence coefficients of genralized Meixner polynomials and Peinlev&eacute; equations
|year=2011 | volume=44 |number=3 | pages=035202 | doi=10.1088/1751-8113/44/3/035202
}}


[[Category:Orthogonal polynomials]]