DLMF:8.17.E21 (Q2662)

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DLMF:8.17.E21
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    Statements

    Defining formula
    I x ⁡ ( a , b ) = I x ⁡ ( a , b + 1 ) - x a ⁢ ( x ′ ) b b ⁢ B ⁡ ( a , b ) . IncI 𝑥 𝑎 𝑏 IncI 𝑥 𝑎 𝑏 1 superscript 𝑥 𝑎 superscript superscript 𝑥 ′ 𝑏 𝑏 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=I_{x}\left(a,b+1\right)-% \frac{x^{a}(x^{\prime})^{b}}{b\mathrm{B}\left(a,b\right)}.}}
    0 references
    DLMF id
    DLMF:8.17.E21
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    Symbols used
    beta function
    Defining formula
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2aedec
    0 references
    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.m2andec
    0 references
     
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