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DLMF:8.17.E8 - MaRDI portal

DLMF:8.17.E8 (Q3346)

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DLMF:8.17.E8
No description defined

    Statements

    DLMF defining formula
    B x ⁡ ( a , b ) = x a ⁢ ( 1 - x ) b a ⁢ F ⁡ ( a + b , 1 ; a + 1 ; x ) , incomplete-Beta 𝑥 𝑎 𝑏 superscript 𝑥 𝑎 superscript 1 𝑥 𝑏 𝑎 Gauss-hypergeometric-F 𝑎 𝑏 1 𝑎 1 𝑥 {\displaystyle{\displaystyle\mathrm{B}_{x}\left(a,b\right)=\frac{x^{a}(1-x)^{b% }}{a}F\left(a+b,1;a+1;x\right),}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    DLMF defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aadec
    0 references
    incomplete beta function
    DLMF defining formula
    B x ⁡ ( a , b ) incomplete-Beta 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right% )}}
    xml-id
    C8.S17.E1.m2acdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1fdec
    0 references
    parameter
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1edec
    0 references
    variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1fdec
    0 references

    Identifiers

     
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