DLMF:18.26.E8 (Q5938)

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DLMF:18.26.E8
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    Statements

    Defining formula
    lim t → ∞ ⁡ S n ⁡ ( ( x - t ) 2 ; λ + i ⁢ t , λ - i ⁢ t , t ⁢ cot ⁡ ϕ ) / t n = n ! ⁢ ( csc ⁡ ϕ ) n ⁢ P n ( λ ) ⁡ ( x ; ϕ ) . subscript → 𝑡 continuous-dual-Hahn-S 𝑛 superscript 𝑥 𝑡 2 𝜆 𝑖 𝑡 𝜆 𝑖 𝑡 𝑡 italic-ϕ superscript 𝑡 𝑛 𝑛 superscript italic-ϕ 𝑛 Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle\lim_{t\to\infty}\ifrac{S_{n}\left((x-t)^{2};% \lambda+it,\lambda-it,t\cot\phi\right)}{t^{n}}=n!(\csc\phi)^{n}P^{(\lambda)}_{% n}\left(x;\phi\right).}}
    0 references
    DLMF id
    DLMF:18.26.E8
    0 references
    Symbols used
    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.m2adec
    0 references
     
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