DLMF:15.4.E31 (Q5015)

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DLMF:15.4.E31
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    Statements

    Defining formula
    F ⁡ ( a , 1 2 + a ; 3 2 - 2 ⁢ a ; - 1 3 ) = ( 8 9 ) - 2 ⁢ a ⁢ Γ ⁡ ( 4 3 ) ⁢ Γ ⁡ ( 3 2 - 2 ⁢ a ) Γ ⁡ ( 3 2 ) ⁢ Γ ⁡ ( 4 3 - 2 ⁢ a ) . Gauss-hypergeometric-F 𝑎 1 2 𝑎 3 2 2 𝑎 1 3 superscript 8 9 2 𝑎 Euler-Gamma 4 3 Euler-Gamma 3 2 2 𝑎 Euler-Gamma 3 2 Euler-Gamma 4 3 2 𝑎 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;\tfrac{3}{2}-2a;-\tfrac{1% }{3}\right)=\left(\frac{8}{9}\right)^{-2a}\frac{\Gamma\left(\tfrac{4}{3}\right% )\Gamma\left(\tfrac{3}{2}-2a\right)}{\Gamma\left(\tfrac{3}{2}\right)\Gamma% \left(\tfrac{4}{3}-2a\right)}.}}
    0 references
    DLMF id
    DLMF:15.4.E31
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
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    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ 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.m2aacdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1xdec
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