DLMF:18.21.E9 (Q5863)

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DLMF:18.21.E9
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    lim a ( 2 a ) 1 2 n C n ( ( 2 a ) 1 2 x + a ; a ) = ( - 1 ) n H n ( x ) . subscript 𝑎 superscript 2 𝑎 1 2 𝑛 Charlier-polynomial-C 𝑛 superscript 2 𝑎 1 2 𝑥 𝑎 𝑎 superscript 1 𝑛 Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{a\to\infty}(2a)^{\frac{1}{2}n}C_{n}\left((2a% )^{\frac{1}{2}}x+a;a\right)=(-1)^{n}H_{n}\left(x\right).}}
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