DLMF:18.21.E8 (Q5862): Difference between revisions

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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.m2adec

Revision as of 01:33, 2 January 2020

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DLMF:18.21.E8
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    Statements

    lim c 1 M n ( ( 1 - c ) - 1 x ; α + 1 , c ) = L n ( α ) ( x ) L n ( α ) ( 0 ) . subscript 𝑐 1 Meixner-polynomial-M 𝑛 superscript 1 𝑐 1 𝑥 𝛼 1 𝑐 Laguerre-polynomial-L 𝛼 𝑛 𝑥 Laguerre-polynomial-L 𝛼 𝑛 0 {\displaystyle{\displaystyle\lim_{c\to 1}M_{n}\left((1-c)^{-1}x;\alpha+1,c% \right)=\frac{L^{(\alpha)}_{n}\left(x\right)}{L^{(\alpha)}_{n}\left(0\right)}.}}
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    DLMF:18.21.E8
    0 references
    L n ( α ) ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    C18.S3.T1.t1.r12.m2adec
    0 references