DLMF:12.7.E2 (Q4125): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11525 / rank
 
Normal rank
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.m2adec

Revision as of 15:11, 2 January 2020

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DLMF:12.7.E2
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    Statements

    Defining formula
    U ⁡ ( - n - 1 2 , z ) = D n ⁡ ( z ) = e - 1 4 ⁢ z 2 ⁢ 𝐻𝑒 n ⁡ ( z ) = 2 - n / 2 ⁢ e - 1 4 ⁢ z 2 ⁢ H n ⁡ ( z / 2 ) , parabolic-U 𝑛 1 2 𝑧 Whittaker-D 𝑛 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Hermite-polynomial-He 𝑛 𝑧 superscript 2 𝑛 2 superscript 𝑒 1 4 superscript 𝑧 2 Hermite-polynomial-H 𝑛 𝑧 2 {\displaystyle{\displaystyle U\left(-n-\tfrac{1}{2},z\right)=D_{n}\left(z% \right)=e^{-\frac{1}{4}z^{2}}\mathit{He}_{n}\left(z\right)=2^{-n/2}e^{-\frac{1% }{4}z^{2}}H_{n}\left(z/\sqrt{2}\right),}}
    0 references
    DLMF id
    DLMF:12.7.E2
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
    0 references
    Symbols used
    Q10922
    Defining formula
    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
    Q11525
    Defining formula
    𝐻𝑒 n ⁡ ( x ) Hermite-polynomial-He 𝑛 𝑥 {\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r14.m2adec
    0 references
     
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