Formula:KLS:09.12:17

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lim_{\alpha\rightarrow\infty} \left(\frac{2}{\alpha}\right)^{\frac{1}{2}n} \Laguerre[\alpha]{n}@{(2\alpha}^{\frac{1}{2}}x+\alpha)=\frac{(-1)^n}{n!}\Hermite{n}@{x} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle L_n^{(\alpha)}}}  : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle H_{n}}}  : Hermite polynomial Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle H_n}}  : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.12 of KLS.

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