DLMF:18.18.E20 (Q5810): 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.m2addec

Revision as of 01:25, 2 January 2020

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DLMF:18.18.E20
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    Statements

    ( 2 x ) n = = 0 n / 2 ( - n ) 2 ! H n - 2 ( x ) . superscript 2 𝑥 𝑛 superscript subscript 0 𝑛 2 Pochhammer 𝑛 2 Hermite-polynomial-H 𝑛 2 𝑥 {\displaystyle{\displaystyle(2x)^{n}=\sum_{\ell=0}^{\left\lfloor n/2\right% \rfloor}\frac{{\left(-n\right)_{2\ell}}}{\ell!}H_{n-2\ell}\left(x\right).}}
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    DLMF:18.18.E20
    0 references
    H n ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r13.m2addec
    0 references