DLMF:18.7.E24 (Q5592): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11475 / rank
 
Normal rank
Property / Symbols used: Q11475 / qualifier
 
Defining formula:

C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11475 / qualifier
 
xml-id: C18.S3.T1.t1.r3.m2afdec

Revision as of 15:22, 2 January 2020

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DLMF:18.7.E24
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    Statements

    Defining formula
    lim λ → ∞ ⁡ λ - 1 2 ⁢ n ⁢ C n ( λ ) ⁡ ( λ - 1 2 ⁢ x ) = H n ⁡ ( x ) n ! . subscript → 𝜆 superscript 𝜆 1 2 𝑛 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 superscript 𝜆 1 2 𝑥 Hermite-polynomial-H 𝑛 𝑥 𝑛 {\displaystyle{\displaystyle\lim_{\lambda\to\infty}\lambda^{-\frac{1}{2}n}C^{(% \lambda)}_{n}\left(\lambda^{-\frac{1}{2}}x\right)=\frac{H_{n}\left(x\right)}{n% !}.}}
    0 references
    DLMF id
    DLMF:18.7.E24
    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.m2aedec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2afdec
    0 references
     
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