DLMF:15.8.E31 (Q5088)

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DLMF:15.8.E31
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    Statements

    Defining formula
    F ⁡ ( 3 ⁢ a , 3 ⁢ a + 1 2 4 ⁢ a + 2 3 ; z ) = ( 1 - 9 8 ⁢ z ) - 2 ⁢ a ⁢ F ⁡ ( a , a + 1 2 2 ⁢ a + 5 6 ; 27 ⁢ z 2 ⁢ ( z - 1 ) ( 9 ⁢ z - 8 ) 2 ) , Gauss-hypergeometric-F 3 𝑎 3 𝑎 1 2 4 𝑎 2 3 𝑧 superscript 1 9 8 𝑧 2 𝑎 Gauss-hypergeometric-F 𝑎 𝑎 1 2 2 𝑎 5 6 27 superscript 𝑧 2 𝑧 1 superscript 9 𝑧 8 2 {\displaystyle{\displaystyle F\left({3a,3a+\frac{1}{2}\atop 4a+\frac{2}{3}};z% \right)=\left(1-\tfrac{9}{8}z\right)^{-2a}\*F\left({a,a+\frac{1}{2}\atop 2a+% \frac{5}{6}};\frac{27z^{2}(z-1)}{(9z-8)^{2}}\right),}}
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    DLMF id
    DLMF:15.8.E31
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    constraint
    ℜ ⁡ z < 8 9 𝑧 8 9 {\displaystyle{\displaystyle\Re z<\frac{8}{9}}}
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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.m2atdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1agdec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1addec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1acdec
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