Meixner 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 , β , γ ) = ∑ k = 0 n ( − 1 ) k ( n k ) ( x k ) k ! ( x + β ) n − k γ − k {\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}}

• Kravchuk polynomials

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• Borodin, Alexei; Olshanski, Grigori (2006). "Meixner polynomials and random partitions". arXiv:math/0609806.
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• Boelen, L.; Filipuk, Galina; Van Assche, Walter (2011). "Recurrence coefficients of generalized Meixner polynomials and Peinlevé equations". J. Phys. A: Math. Theor. 44 (3) 035202. Bibcode:2011JPhA...44c5202B. doi:10.1088/1751-8113/44/3/035202.
• Wang, Xiang-Sheng; Wong, Roderick (2011). "Global asymptotics of the Meixner polynomials". Asymptot. Anal. 75 (3–4): 211–231. arXiv:1101.4370. doi:10.3233/ASY-2011-1060.