DLMF:18.11.E7 (Q5641): Difference between revisions

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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.m2aadec

Revision as of 15:30, 2 January 2020

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DLMF:18.11.E7
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    Statements

    lim n ( - 1 ) n n 1 2 2 2 n n ! H 2 n ( z 2 n 1 2 ) = 1 π 1 2 cos z , subscript 𝑛 superscript 1 𝑛 superscript 𝑛 1 2 superscript 2 2 𝑛 𝑛 Hermite-polynomial-H 2 𝑛 𝑧 2 superscript 𝑛 1 2 1 superscript 𝜋 1 2 𝑧 {\displaystyle{\displaystyle\lim_{n\to\infty}\frac{(-1)^{n}n^{\frac{1}{2}}}{2^% {2n}n!}H_{2n}\left(\frac{z}{2n^{\frac{1}{2}}}\right)=\frac{1}{\pi^{\frac{1}{2}% }}\cos z,}}
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    DLMF:18.11.E7
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    H n ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r13.m2aadec
    0 references