DLMF:18.7.E21 (Q5589)

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DLMF:18.7.E21
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    Statements

    Defining formula
    lim β → ∞ ⁡ P n ( α , β ) ⁡ ( 1 - ( 2 ⁢ x / β ) ) = L n ( α ) ⁡ ( x ) . subscript → 𝛽 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 2 𝑥 𝛽 Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\beta\to\infty}P^{(\alpha,\beta)}_{n}\left(1% -(\ifrac{2x}{\beta})\right)=L^{(\alpha)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.7.E21
    0 references
    Symbols used
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2akdec
    0 references
    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.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1tdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1tdec
    0 references
     
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