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DLMF:18.9.E14 - MaRDI portal

DLMF:18.9.E14 (Q6307)

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DLMF:18.9.E14
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    Statements

    DLMF defining formula
    x ⁢ L n ( α + 1 ) ⁡ ( x ) = - ( n + 1 ) ⁢ L n + 1 ( α ) ⁡ ( x ) + ( n + α + 1 ) ⁢ L n ( α ) ⁡ ( x ) . 𝑥 Laguerre-polynomial-L 𝛼 1 𝑛 𝑥 𝑛 1 Laguerre-polynomial-L 𝛼 𝑛 1 𝑥 𝑛 𝛼 1 Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle xL^{(\alpha+1)}_{n}\left(x\right)=-(n+1)L^{(% \alpha)}_{n+1}\left(x\right)+(n+\alpha+1)L^{(\alpha)}_{n}\left(x\right).}}
    0 references
    Symbols used
    Laguerre (or generalized Laguerre) polynomial
    DLMF 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.m2abdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ndec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1mdec
    0 references

    Identifiers

     
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