DLMF:15.16.E5 (Q5182)

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DLMF:15.16.E5
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    Defining formula
    F ⁡ ( 1 2 + λ , - 1 2 - ν 1 + λ + μ ; z ) ⁢ F ⁡ ( 1 2 - λ , 1 2 + ν 1 + ν + μ ; 1 - z ) + F ⁡ ( 1 2 + λ , 1 2 - ν 1 + λ + μ ; z ) ⁢ F ⁡ ( - 1 2 - λ , 1 2 + ν 1 + ν + μ ; 1 - z ) - F ⁡ ( 1 2 + λ , 1 2 - ν 1 + λ + μ ; z ) ⁢ F ⁡ ( 1 2 - λ , 1 2 + ν 1 + ν + μ ; 1 - z ) = Γ ⁡ ( 1 + λ + μ ) ⁢ Γ ⁡ ( 1 + ν + μ ) Γ ⁡ ( λ + μ + ν + 3 2 ) ⁢ Γ ⁡ ( 1 2 + ν ) , Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜆 𝜇 𝑧 Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜈 𝜇 1 𝑧 Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜆 𝜇 𝑧 Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜈 𝜇 1 𝑧 Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜆 𝜇 𝑧 Gauss-hypergeometric-F 1 2 𝜆 1 2 𝜈 1 𝜈 𝜇 1 𝑧 Euler-Gamma 1 𝜆 𝜇 Euler-Gamma 1 𝜈 𝜇 Euler-Gamma 𝜆 𝜇 𝜈 3 2 Euler-Gamma 1 2 𝜈 {\displaystyle{\displaystyle F\left({\frac{1}{2}+\lambda,-\frac{1}{2}-\nu\atop 1% +\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+% \mu};1-z\right)+F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu% };z\right)F\left({-\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z% \right)-F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z% \right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)=% \frac{\Gamma\left(1+\lambda+\mu\right)\Gamma\left(1+\nu+\mu\right)}{\Gamma% \left(\lambda+\mu+\nu+\frac{3}{2}\right)\Gamma\left(\frac{1}{2}+\nu\right)},}}
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    DLMF id
    DLMF:15.16.E5
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