DLMF:15.4.E31 (Q5015)

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DLMF:15.4.E31
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    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)}.}}
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    DLMF:15.4.E31
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