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DLMF:26.3.E4 - MaRDI portal

DLMF:26.3.E4 (Q8470)

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DLMF:26.3.E4
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    Statements

    DLMF defining formula
    ∑ m = 0 ∞ ( m + n m ) ⁢ x m = 1 ( 1 - x ) n + 1 , superscript subscript 𝑚 0 binomial 𝑚 𝑛 𝑚 superscript 𝑥 𝑚 1 superscript 1 𝑥 𝑛 1 {\displaystyle{\displaystyle\sum_{m=0}^{\infty}\genfrac{(}{)}{0.0pt}{}{m+n}{m}% x^{m}=\frac{1}{(1-x)^{n+1}},}}
    0 references
    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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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.m1aedec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1adec
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    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1edec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1edec
    0 references
     
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