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DLMF:18.35.E9 - MaRDI portal

DLMF:18.35.E9 (Q6744)

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DLMF:18.35.E9
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    Statements

    DLMF defining formula
    P n ( λ ) ⁡ ( cos ⁡ ϕ ; 0 , x ⁢ sin ⁡ ϕ ) = P n ( λ ) ⁡ ( x ; ϕ ) . Pollaczek-polynomial-P 𝜆 𝑛 italic-ϕ 0 𝑥 italic-ϕ Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\lambda)}_{n}\left(\cos\phi;0,x\sin\phi\right% )=P^{(\lambda)}_{n}\left(x;\phi\right).}}
    0 references
    Symbols used
    Meixner–Pollaczek polynomial
    DLMF 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
    Pollaczek polynomial
    DLMF defining formula
    P n ( λ ) ⁡ ( x ; a , b ) Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{a},\NVar{b}\right)}}
    xml-id
    C18.S35.E4.m2afdec
    0 references
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references

    Identifiers

     
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