DLMF:17.2.E36 (Q5326)

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DLMF:17.2.E36
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    Statements

    Defining formula
    ∑ j = 0 n ( n j ) ⁢ ( - z ) j = ( 1 - z ) n . superscript subscript 𝑗 0 𝑛 binomial 𝑛 𝑗 superscript 𝑧 𝑗 superscript 1 𝑧 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{j}(-z)^{j% }=(1-z)^{n}.}}
    0 references
    DLMF id
    DLMF:17.2.E36
    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.m1aldec
    0 references
    Q11712
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C17.S1.XMD2.m1fdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1afdec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1adec
    0 references
     
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