DLMF:18.21.E10 (Q5864)

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DLMF:18.21.E10
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    Defining formula
    lim t → ∞ ⁡ t - n ⁢ p n ⁡ ( x - t ; λ + i ⁢ t , - t ⁢ tan ⁡ ϕ , λ - i ⁢ t , - t ⁢ tan ⁡ ϕ ) = ( - 1 ) n ( cos ⁡ ϕ ) n ⁢ P n ( λ ) ⁡ ( x ; ϕ ) . subscript → 𝑡 superscript 𝑡 𝑛 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑡 𝜆 𝑖 𝑡 𝑡 italic-ϕ 𝜆 𝑖 𝑡 𝑡 italic-ϕ superscript 1 𝑛 superscript italic-ϕ 𝑛 Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle\lim_{t\to\infty}t^{-n}p_{n}\left(x-t;\lambda+it,-% t\tan\phi,\lambda-it,-t\tan\phi\right)=\frac{(-1)^{n}}{(\cos\phi)^{n}}P^{(% \lambda)}_{n}\left(x;\phi\right).}}
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    DLMF id
    DLMF:18.21.E10
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