DLMF:18.7.E26 (Q5594): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10922 / rank
 
Normal rank
Property / Symbols used: Q10922 / qualifier
 
Defining formula:

H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}

\HermitepolyH{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10922 / qualifier
 
xml-id: C18.S3.T1.t1.r13.m2afdec

Revision as of 15:22, 2 January 2020

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DLMF:18.7.E26
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    Statements

    Defining formula
    lim α → ∞ ⁡ ( 2 α ) 1 2 ⁢ n ⁢ L n ( α ) ⁡ ( ( 2 ⁢ α ) 1 2 ⁢ x + α ) = ( - 1 ) n n ! ⁢ H n ⁡ ( x ) . subscript → 𝛼 superscript 2 𝛼 1 2 𝑛 Laguerre-polynomial-L 𝛼 𝑛 superscript 2 𝛼 1 2 𝑥 𝛼 superscript 1 𝑛 𝑛 Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\left(\frac{2}{\alpha}\right% )^{\frac{1}{2}n}L^{(\alpha)}_{n}\left((2\alpha)^{\frac{1}{2}}x+\alpha\right)=% \frac{(-1)^{n}}{n!}H_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.7.E26
    0 references
    Symbols used
    Q10922
    Defining formula
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2afdec
    0 references
     
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