DLMF:26.6.E1 (Q7803)

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DLMF:26.6.E1
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    Statements

    Defining formula
    D ⁢ ( m , n ) = ∑ k = 0 n ( n k ) ⁢ ( m + n - k n ) = ∑ k = 0 n 2 k ⁢ ( m k ) ⁢ ( n k ) . 𝐷 𝑚 𝑛 superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 binomial 𝑚 𝑛 𝑘 𝑛 superscript subscript 𝑘 0 𝑛 superscript 2 𝑘 binomial 𝑚 𝑘 binomial 𝑛 𝑘 {\displaystyle{\displaystyle D(m,n)=\sum_{k=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{k% }\genfrac{(}{)}{0.0pt}{}{m+n-k}{n}=\sum_{k=0}^{n}2^{k}\genfrac{(}{)}{0.0pt}{}{% m}{k}\genfrac{(}{)}{0.0pt}{}{n}{k}.}}
    0 references
    DLMF id
    DLMF:26.6.E1
    0 references
    Symbols used
    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
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1dec
    0 references
    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1dec
    0 references
     
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