DLMF:18.17.E23 (Q5764): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2addec

Revision as of 15:50, 2 January 2020

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DLMF:18.17.E23
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    Statements

    0 e - 1 2 x 2 𝐻𝑒 2 n ( x ) cos ( x y ) d x = ( - 1 ) n 1 2 π y 2 n e - 1 2 y 2 , superscript subscript 0 superscript 𝑒 1 2 superscript 𝑥 2 Hermite-polynomial-He 2 𝑛 𝑥 𝑥 𝑦 𝑥 superscript 1 𝑛 1 2 𝜋 superscript 𝑦 2 𝑛 superscript 𝑒 1 2 superscript 𝑦 2 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{1}{2}x^{2}}\mathit{He}_% {2n}\left(x\right)\cos\left(xy\right)\mathrm{d}x=(-1)^{n}\sqrt{\tfrac{1}{2}\pi% }y^{2n}e^{-\frac{1}{2}y^{2}},}}
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    DLMF:18.17.E23
    0 references
    𝐻𝑒 n ( x ) Hermite-polynomial-He 𝑛 𝑥 {\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r14.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ajdec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2addec
    0 references