DLMF:18.18.E19 (Q5809): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1odec

Latest revision as of 01:25, 2 January 2020

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DLMF:18.18.E19
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    Statements

    x n = ( α + 1 ) n = 0 n ( - n ) ( α + 1 ) L ( α ) ( x ) . superscript 𝑥 𝑛 Pochhammer 𝛼 1 𝑛 superscript subscript 0 𝑛 Pochhammer 𝑛 Pochhammer 𝛼 1 Laguerre-polynomial-L 𝛼 𝑥 {\displaystyle{\displaystyle x^{n}={\left(\alpha+1\right)_{n}}\sum_{\ell=0}^{n% }\frac{{\left(-n\right)_{\ell}}}{{\left(\alpha+1\right)_{\ell}}}L^{(\alpha)}_{% \ell}\left(x\right).}}
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    DLMF:18.18.E19
    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.m2aedec
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    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1agdec
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    {\displaystyle{\displaystyle\ell}}
    C18.S1.XMD4.m1idec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1rdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1odec
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