DLMF:18.5.E12 (Q5520): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1ldec
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.m1kdec

Latest revision as of 15:17, 2 January 2020

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DLMF:18.5.E12
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    Statements

    L n ( α ) ( x ) = = 0 n ( α + + 1 ) n - ( n - ) ! ! ( - x ) = ( α + 1 ) n n ! F 1 1 ( - n α + 1 ; x ) . Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript subscript 0 𝑛 Pochhammer 𝛼 1 𝑛 𝑛 superscript 𝑥 Pochhammer 𝛼 1 𝑛 𝑛 Kummer-confluent-hypergeometric-M-as-1F1 𝑛 𝛼 1 𝑥 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\sum_{\ell=0}^{n}% \frac{{\left(\alpha+\ell+1\right)_{n-\ell}}}{(n-\ell)!\;\ell!}(-x)^{\ell}=% \frac{{\left(\alpha+1\right)_{n}}}{n!}{{}_{1}F_{1}}\left({-n\atop\alpha+1};x% \right).}}
    0 references
    DLMF:18.5.E12
    0 references
    F 1 1 ( a ; b ; z ) Kummer-confluent-hypergeometric-M-as-1F1 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}% \right)}}
    C16.S2.m7adec
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    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.m2abdec
    0 references
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1afdec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5agdec
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    {\displaystyle{\displaystyle\ell}}
    C18.S1.XMD4.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1ldec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1kdec
    0 references