DLMF:26.3.E10 (Q7783)

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DLMF:26.3.E10
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    Statements

    Defining formula
    ( m n ) = ∑ k = 0 n ( - 1 ) n - k ⁢ ( m + 1 k ) , binomial 𝑚 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑛 𝑘 binomial 𝑚 1 𝑘 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{m}{n}=\sum_{k=0}^{n}(-1)^{% n-k}\genfrac{(}{)}{0.0pt}{}{m+1}{k},}}
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    DLMF id
    DLMF:26.3.E10
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    constraint
    m ≥ n ≥ 0 𝑚 𝑛 0 {\displaystyle{\displaystyle m\geq n\geq 0}}
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    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1akdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1bdec
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    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1jdec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1kdec
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