DLMF:8.17.E20 (Q2661)

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DLMF:8.17.E20
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    Statements

    Defining formula
    I x ⁡ ( a , b ) = I x ⁡ ( a + 1 , b ) + x a ⁢ ( x ′ ) b a ⁢ B ⁡ ( a , b ) , IncI 𝑥 𝑎 𝑏 IncI 𝑥 𝑎 1 𝑏 superscript 𝑥 𝑎 superscript superscript 𝑥 ′ 𝑏 𝑎 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=I_{x}\left(a+1,b\right)+% \frac{x^{a}(x^{\prime})^{b}}{a\mathrm{B}\left(a,b\right)},}}
    0 references
    DLMF id
    DLMF:8.17.E20
    0 references
    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.m2addec
    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.m2amdec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1qdec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1pdec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1qdec
    0 references
    Q11367
    Defining formula
    x ′ superscript 𝑥 ′ {\displaystyle{\displaystyle x^{\prime}}}
    xml-id
    C8.S17.XMD9.m1fdec
    0 references
     
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