DLMF:18.21.E12 (Q5866)

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DLMF:18.21.E12
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    Statements

    Defining formula
    lim ϕ → 0 ⁡ P n ( 1 2 ⁢ α + 1 2 ) ⁡ ( - ( 2 ⁢ ϕ ) - 1 ⁢ x ; ϕ ) = L n ( α ) ⁡ ( x ) . subscript → italic-ϕ 0 Meixner-Pollaczek-polynomial-P 1 2 𝛼 1 2 𝑛 superscript 2 italic-ϕ 1 𝑥 italic-ϕ Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\phi\to 0}P^{(\frac{1}{2}\alpha+\frac{1}{2})% }_{n}\left(-(2\phi)^{-1}x;\phi\right)=L^{(\alpha)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.21.E12
    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.m2aadec
    0 references
    Q11664
    Defining formula
    P n ( λ ) ⁡ ( x ; ϕ ) Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}
    xml-id
    C18.S19.Px3.p1.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1kdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1kdec
    0 references
     
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