DLMF:18.22.E30 (Q5901)

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DLMF:18.22.E30
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    Statements

    Defining formula
    δ x ( w ( λ + 1 2 ) ⁢ ( x ; ϕ ) ⁢ P n ( λ + 1 2 ) ⁡ ( x ; ϕ ) ) = - ( n + 1 ) ⁢ w ( λ ) ⁢ ( x ; ϕ ) ⁢ P n + 1 ( λ ) ⁡ ( x ; ϕ ) . central-difference 𝑥 superscript 𝑤 𝜆 1 2 𝑥 italic-ϕ Meixner-Pollaczek-polynomial-P 𝜆 1 2 𝑛 𝑥 italic-ϕ 𝑛 1 superscript 𝑤 𝜆 𝑥 italic-ϕ Meixner-Pollaczek-polynomial-P 𝜆 𝑛 1 𝑥 italic-ϕ {\displaystyle{\displaystyle\delta_{x}\left(w^{(\lambda+\frac{1}{2})}(x;\phi)P% ^{(\lambda+\frac{1}{2})}_{n}\left(x;\phi\right)\right)=-(n+1)w^{(\lambda)}(x;% \phi)P^{(\lambda)}_{n+1}\left(x;\phi\right).}}
    0 references
    DLMF id
    DLMF:18.22.E30
    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.m2acdec
    0 references
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1acdec
    0 references
    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1abdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1acdec
    0 references
     
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