查看“︁梅西纳多项式”︁的源代码

[[File:Meixner 2.gif|thumb|Meixner  polynomials  3D  animation]]
[[File:Meixner 3.gif|thumb|Meixner  polynomials  3D  animation]]
[[File:Meixner 4.gif|thumb|Meixner  polynomials  3D  animation]]

'''梅西纳多项式'''定义为

:<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>

梅西纳多项式的前几项为：

<math>Mx[1] := [-\beta-(1-\gamma)*x/\gamma]</math>

<math>Mx[2] := [(\gamma^2*\beta^2-\beta*\gamma^2)/\gamma^2+(\gamma^2-2*\beta*\gamma^2-1+2*\gamma*\beta)*x/\gamma^2+(-2*\gamma+1+\gamma^2)*x^2/\gamma^2]</math>

<math>Mx[3] := [-(\gamma^3*\beta^3-3*\gamma^3*\beta^2+2*\gamma^3*\beta)/\gamma^3-(-3*\gamma^3*\beta^2+3*\gamma^2*\beta^2-3*\gamma*\beta+6*\gamma^3*\beta-2*\gamma^3-3*\beta*\gamma^2+2)*x/\gamma^3-(-3*\gamma^3+3*\gamma^3*\beta+3*\gamma^2-6*\beta*\gamma^2+3*\gamma*\beta-3+3*\gamma)*x^2/\gamma^3-(3*\gamma^2-3*\gamma-\gamma^3+1)*x^3/\gamma^3]</math>

==参考文献==
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*{{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
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}}
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|doi=10.1007/BFb0076530
}}
*{{cite journal | first1= M. V. | last1=Tratnik
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|year=1989 | journal= J. Math. Phys. | volume=30 | number=12 | pages=2740 | doi=10.1063/1.528507 
}}
*{{cite journal | first1= M. V. | last1=Tratnik
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*{{cite journal | first1=H. | last1=Bavinck | first2=H. | last2=Vanhaeringen
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|journal= J. Math. Anal. Applic. | year=1994 | volume=184 | number=3
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*{{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 | author= | access-date=2015-01-27 | archive-url=https://web.archive.org/web/20081122043419/http://www.emis.ams.org/journals/ETNA/vol.9.1999/pp1-25.dir/pp1-25.pdf | archive-date=2008-11-22 | dead-url=yes }}
*{{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 |last2=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:正交多项式]]