DLMF:8.17.E7 (Q2647)

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DLMF:8.17.E7
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    Statements

    Defining formula
    B x ⁡ ( a , b ) = x a a ⁢ F ⁡ ( a , 1 - b ; a + 1 ; x ) , incomplete-Beta 𝑥 𝑎 𝑏 superscript 𝑥 𝑎 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑎 1 𝑥 {\displaystyle{\displaystyle\mathrm{B}_{x}\left(a,b\right)=\frac{x^{a}}{a}F% \left(a,1-b;a+1;x\right),}}
    0 references
    DLMF id
    DLMF:8.17.E7
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    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.m2adec
    0 references
    incomplete beta function
    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.m2abdec
    0 references
     
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