DLMF:15.4.E19 (Q5003)

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DLMF:15.4.E19
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    Statements

    Defining formula
    F ⁡ ( a + 1 , b ; a ; z ) = ( 1 - ( 1 - ( b / a ) ) ⁢ z ) ⁢ ( 1 - z ) - 1 - b . Gauss-hypergeometric-F 𝑎 1 𝑏 𝑎 𝑧 1 1 𝑏 𝑎 𝑧 superscript 1 𝑧 1 𝑏 {\displaystyle{\displaystyle F\left(a+1,b;a;z\right)=\left(1-(1-(\ifrac{b}{a})% )z\right)(1-z)^{-1-b}.}}
    0 references
    DLMF id
    DLMF:15.4.E19
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    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.m2ardec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1rdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1mdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1adec
    0 references
     
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