DLMF:18.18.E38 (Q5828): Difference between revisions

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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.m1akdec
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.m1agdec

Latest revision as of 01:28, 2 January 2020

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DLMF:18.18.E38
No description defined

    Statements

    Defining formula
    ∑ ℓ = 0 n L ℓ ( α ) ⁡ ( x ) ⁢ L n - ℓ ( β ) ⁡ ( y ) = L n ( α + β + 1 ) ⁡ ( x + y ) . superscript subscript ℓ 0 𝑛 Laguerre-polynomial-L 𝛼 ℓ 𝑥 Laguerre-polynomial-L 𝛽 𝑛 ℓ 𝑦 Laguerre-polynomial-L 𝛼 𝛽 1 𝑛 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}L^{(\alpha)}_{\ell}\left(x\right)% L^{(\beta)}_{n-\ell}\left(y\right)=L^{(\alpha+\beta+1)}_{n}\left(x+y\right).}}
    0 references
    DLMF id
    DLMF:18.18.E38
    0 references
    Symbols used
    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.m2ahdec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1cdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1ydec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1akdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1agdec
    0 references
     
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