Formula:KLS:09.14:05: Difference between revisions

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C n ⁡ ( x ; a ) = ( - 1 a ) n ⁢ C ^ n ⁡ ( x ) Charlier-polynomial-C 𝑛 𝑥 𝑎 superscript 1 𝑎 𝑛 Charlier-polynomial-monic-p 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle{\displaystyle C_{n}\!\left(x;a\right)=\left(-% \frac{1}{a}\right)^{n}{\widehat{C}}_{n}\!\left(x\right)}}}

Proof

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Symbols List

C n subscript 𝐶 𝑛 {\displaystyle{\displaystyle{\displaystyle C_{n}}}}  : Charlier polynomial : http://dlmf.nist.gov/18.19#T1.t1.r11
C ^ n subscript ^ 𝐶 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}}}}  : monic Charlier polynomial : http://drmf.wmflabs.org/wiki/Definition:monicCharlier

Bibliography

Equation in Section 9.14 of KLS.

URL links

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