DLMF:8.17.E24 (Q2666)

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DLMF:8.17.E24
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    Statements

    Defining formula
    I x ⁡ ( m , n ) = ( 1 - x ) n ⁢ ∑ j = m ∞ ( n + j - 1 j ) ⁢ x j , IncI 𝑥 𝑚 𝑛 superscript 1 𝑥 𝑛 superscript subscript 𝑗 𝑚 binomial 𝑛 𝑗 1 𝑗 superscript 𝑥 𝑗 {\displaystyle{\displaystyle I_{x}\left(m,n\right)=(1-x)^{n}\sum_{j=m}^{\infty% }\genfrac{(}{)}{0.0pt}{}{n+j-1}{j}x^{j},}}
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    DLMF id
    DLMF:8.17.E24
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    constraint
    0 ≤ x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0\leq x<1}}
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    Symbols used
    incomplete beta function
    Defining formula
    I x ⁡ ( a , b ) IncI 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C8.S17.E2.m2apdec
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    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
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    Q11329
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1adec
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