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DLMF:26.3.E3 - MaRDI portal

DLMF:26.3.E3 (Q8469)

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DLMF:26.3.E3
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    Statements

    DLMF defining formula
    ∑ n = 0 m ( m n ) ⁢ x n = ( 1 + x ) m , superscript subscript 𝑛 0 𝑚 binomial 𝑚 𝑛 superscript 𝑥 𝑛 superscript 1 𝑥 𝑚 {\displaystyle{\displaystyle\sum_{n=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{n}x^{n}=(% 1+x)^{m},}}
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    constraint
    m = 0 , 1 , … 𝑚 0 1 … {\displaystyle{\displaystyle m=0,1,\ldots}}
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    Symbols used
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1dec
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    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1ddec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1ddec
    0 references
     
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