DLMF:18.21.E6 (Q5860)

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DLMF:18.21.E6
No description defined

    Statements

    Defining formula
    lim N → ∞ ⁡ K n ⁡ ( x ; N - 1 ⁢ a , N ) = C n ⁡ ( x ; a ) . subscript → 𝑁 Krawtchouk-polynomial-K 𝑛 𝑥 superscript 𝑁 1 𝑎 𝑁 Charlier-polynomial-C 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle\lim_{N\to\infty}K_{n}\left(x;N^{-1}a,N\right)=C_{% n}\left(x;a\right).}}
    0 references
    DLMF id
    DLMF:18.21.E6
    0 references
    Symbols used
    Q11565
    Defining formula
    C n ⁡ ( x ; a ) Charlier-polynomial-C 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    xml-id
    C18.S19.T1.t1.r5.m2aadec
    0 references
    Q11662
    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.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1edec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references
     
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