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DLMF:18.21.E3 - MaRDI portal

DLMF:18.21.E3 (Q6553)

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DLMF:18.21.E3
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    Statements

    DLMF defining formula
    lim t → ∞ ⁡ Q n ⁡ ( x ; p ⁢ t , ( 1 - p ) ⁢ t , N ) = K n ⁡ ( x ; p , N ) . subscript → 𝑡 Hahn-polynomial-Q 𝑛 𝑥 𝑝 𝑡 1 𝑝 𝑡 𝑁 Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 {\displaystyle{\displaystyle\lim_{t\to\infty}Q_{n}\left(x;pt,(1-p)t,N\right)=K% _{n}\left(x;p,N\right).}}
    0 references
    Symbols used
    Hahn polynomial
    DLMF defining formula
    Q n ⁡ ( x ; α , β , N ) Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{N}\right)}}
    xml-id
    C18.S19.T1.t1.r2.m1aadec
    0 references
    Krawtchouk polynomial
    DLMF defining formula
    K n ⁡ ( x ; p , N ) Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 {\displaystyle{\displaystyle K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}% \right)}}
    xml-id
    C18.S19.T1.t1.r3.p1.m2aadec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    positive integer
    DLMF defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1bdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1bdec
    0 references

    Identifiers

     
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