DLMF:18.21.E9 (Q5863): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10922 / rank
 
Normal rank
Property / Symbols used: Q10922 / qualifier
 
test:

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.m2adec

Revision as of 00:33, 2 January 2020

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DLMF:18.21.E9
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    Statements

    test
    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).}}
    0 references
    DLMF id
    DLMF:18.21.E9
    0 references
    Symbols used
    Q11565
    test
    C n ⁡ ( x ; a ) Charlier-polynomial-C 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    xml-id
    C18.S19.T1.t1.r5.m2acdec
    0 references
    Q10922
    test
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2adec
    0 references
     
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