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DLMF:18.21.E8 - MaRDI portal

DLMF:18.21.E8 (Q6558)

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DLMF:18.21.E8
No description defined

    Statements

    DLMF defining formula
    lim c → 1 ⁡ M n ⁡ ( ( 1 - c ) - 1 ⁢ x ; α + 1 , c ) = L n ( α ) ⁡ ( x ) L n ( α ) ⁡ ( 0 ) . subscript → 𝑐 1 Meixner-polynomial-M 𝑛 superscript 1 𝑐 1 𝑥 𝛼 1 𝑐 Laguerre-polynomial-L 𝛼 𝑛 𝑥 Laguerre-polynomial-L 𝛼 𝑛 0 {\displaystyle{\displaystyle\lim_{c\to 1}M_{n}\left((1-c)^{-1}x;\alpha+1,c% \right)=\frac{L^{(\alpha)}_{n}\left(x\right)}{L^{(\alpha)}_{n}\left(0\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.m2adec
    0 references
    Meixner polynomial
    DLMF defining formula
    M n ⁡ ( x ; β , c ) Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle M_{\NVar{n}}\left(\NVar{x};\NVar{\beta},\NVar{c}% \right)}}
    xml-id
    C18.S19.T1.t1.r4.m2acdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1gdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1gdec
    0 references

    Identifiers

     
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