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DLMF:18.18.E10 - MaRDI portal

DLMF:18.18.E10 (Q6497)

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DLMF:18.18.E10
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    Statements

    DLMF defining formula
    L n ( α 1 + … + α r + r - 1 ) ⁡ ( x 1 + … + x r ) = ∑ m 1 + … + m r = n L m 1 ( α 1 ) ⁡ ( x 1 ) ⁢ ⋯ ⁢ L m r ( α r ) ⁡ ( x r ) . Laguerre-polynomial-L subscript 𝛼 1 … subscript 𝛼 𝑟 𝑟 1 𝑛 subscript 𝑥 1 … subscript 𝑥 𝑟 subscript subscript 𝑚 1 … subscript 𝑚 𝑟 𝑛 Laguerre-polynomial-L subscript 𝛼 1 subscript 𝑚 1 subscript 𝑥 1 ⋯ Laguerre-polynomial-L subscript 𝛼 𝑟 subscript 𝑚 𝑟 subscript 𝑥 𝑟 {\displaystyle{\displaystyle L^{(\alpha_{1}+\dots+\alpha_{r}+r-1)}_{n}\left(x_% {1}+\dots+x_{r}\right)=\sum_{m_{1}+\dots+m_{r}=n}L^{(\alpha_{1})}_{m_{1}}\left% (x_{1}\right)\cdots L^{(\alpha_{r})}_{m_{r}}\left(x_{r}\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
    0 references
    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1idec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1fdec
    0 references

    Identifiers

     
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