DLMF:18.20.E4 (Q5845)

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DLMF:18.20.E4
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    Statements

    Defining formula
    w ( λ ) ⁢ ( x ; ϕ ) ⁢ P n ( λ ) ⁡ ( x ; ϕ ) = 1 n ! ⁢ δ x n ( w ( λ + 1 2 ⁢ n ) ⁢ ( x ; ϕ ) ) . superscript 𝑤 𝜆 𝑥 italic-ϕ Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ 1 𝑛 superscript central-difference 𝑥 𝑛 superscript 𝑤 𝜆 1 2 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle w^{(\lambda)}(x;\phi)P^{(\lambda)}_{n}\left(x;% \phi\right)=\frac{1}{n!}\delta_{x}^{n}\left(w^{(\lambda+\frac{1}{2}n)}(x;\phi)% \right).}}
    0 references
    DLMF id
    DLMF:18.20.E4
    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
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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