DLMF:26.14.E5 (Q7956)

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DLMF:26.14.E5
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    Statements

    Defining formula
    ∑ k = 0 n - 1 ⟨ n k ⟩ ⁢ ( x + k n ) = x n . superscript subscript 𝑘 0 𝑛 1 Eulerian-number 𝑛 𝑘 binomial 𝑥 𝑘 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}\genfrac{<}{>}{0.0pt}{}{n}{k}% \genfrac{(}{)}{0.0pt}{}{x+k}{n}=x^{n}.}}
    0 references
    DLMF id
    DLMF:26.14.E5
    0 references
    Symbols used
    Q12217
    Defining formula
    ⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    xml-id
    C26.S14.SS1.p3.m2abdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q12173
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1adec
    0 references
     
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