DLMF:18.9.E28 (Q5624): Difference between revisions

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Property / Symbols used: Q11525 / rank
 
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Property / Symbols used: Q11525 / qualifier
 
Defining formula:

𝐻𝑒 n ( x ) Hermite-polynomial-He 𝑛 𝑥 {\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}

\dilHermitepolyHe{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11525 / qualifier
 
xml-id: C18.S3.T1.t1.r14.m2abdec

Revision as of 15:25, 2 January 2020

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DLMF:18.9.E28
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    Statements

    d d x ( e - 1 2 x 2 𝐻𝑒 n ( x ) ) = - e - 1 2 x 2 𝐻𝑒 n + 1 ( x ) . derivative 𝑥 superscript 𝑒 1 2 superscript 𝑥 2 Hermite-polynomial-He 𝑛 𝑥 superscript 𝑒 1 2 superscript 𝑥 2 Hermite-polynomial-He 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{-\frac{1}{2% }x^{2}}\mathit{He}_{n}\left(x\right)\right)=-e^{-\frac{1}{2}x^{2}}\mathit{He}_% {n+1}\left(x\right).}}
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    DLMF:18.9.E28
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    𝐻𝑒 n ( x ) Hermite-polynomial-He 𝑛 𝑥 {\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r14.m2abdec
    0 references