Formula:KLS:09.10:05

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M n ⁡ ( x ; β , c ) = 1 ( β ) n ⁢ ( c - 1 c ) n ⁢ M ^ n ⁡ ( x ; β , c ) Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 1 Pochhammer-symbol 𝛽 𝑛 superscript 𝑐 1 𝑐 𝑛 Meixner-polynomial-monic-p 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle{\displaystyle M_{n}\!\left(x;\beta,c\right)=\frac% {1}{{\left(\beta\right)_{n}}}\left(\frac{c-1}{c}\right)^{n}{\widehat{M}}_{n}\!% \left(x;\beta,c\right)}}}

Proof

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Symbols List

M n subscript 𝑀 𝑛 {\displaystyle{\displaystyle{\displaystyle M_{n}}}}  : Meixner polynomial : http://dlmf.nist.gov/18.19#T1.t1.r9
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
M ^ n subscript ^ 𝑀 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}}}}  : monic Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:monicMeixner

Bibliography

Equation in Section 9.10 of KLS.

URL links

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