DLMF:18.22.E21 (Q5892)

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DLMF:18.22.E21
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    Statements

    Defining formula
    Δ x K n ⁡ ( x ; p , N ) = - n p ⁢ N ⁢ K n - 1 ⁡ ( x ; p , N - 1 ) , forward-difference 𝑥 Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 𝑛 𝑝 𝑁 Krawtchouk-polynomial-K 𝑛 1 𝑥 𝑝 𝑁 1 {\displaystyle{\displaystyle\Delta_{x}K_{n}\left(x;p,N\right)=-\frac{n}{pN}K_{% n-1}\left(x;p,N-1\right),}}
    0 references
    DLMF id
    DLMF:18.22.E21
    0 references
    Symbols used
    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
    Q11097
    Defining formula
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    xml-id
    C3.S6.SS1.p1.m2aadec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1sdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1hdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1tdec
    0 references
     
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