DLMF:18.11.E6 (Q5640): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11333 / rank
 
Normal rank
Property / Symbols used: Q11333 / qualifier
 
Defining formula:

L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11333 / qualifier
 
xml-id: C18.S3.T1.t1.r12.m2aadec

Revision as of 15:30, 2 January 2020

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DLMF:18.11.E6
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    Statements

    Defining formula
    lim n → ∞ ⁡ 1 n α ⁢ L n ( α ) ⁡ ( z n ) = 1 z 1 2 ⁢ α ⁢ J α ⁡ ( 2 ⁢ z 1 2 ) . subscript → 𝑛 1 superscript 𝑛 𝛼 Laguerre-polynomial-L 𝛼 𝑛 𝑧 𝑛 1 superscript 𝑧 1 2 𝛼 Bessel-J 𝛼 2 superscript 𝑧 1 2 {\displaystyle{\displaystyle\lim_{n\to\infty}\frac{1}{n^{\alpha}}L^{(\alpha)}_% {n}\left(\frac{z}{n}\right)=\frac{1}{z^{\frac{1}{2}\alpha}}J_{\alpha}\left(2z^% {\frac{1}{2}}\right).}}
    0 references
    DLMF id
    DLMF:18.11.E6
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    Q11333
    Defining formula
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2aadec
    0 references
     
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