DLMF:15.10.E35 (Q5151)

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DLMF:15.10.E35
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    w 2 ( z ) = e ( 1 - a ) π i Γ ( 2 - c ) Γ ( c - b ) Γ ( a - c + 1 ) Γ ( c - a - b + 1 ) w 4 ( z ) + e - a π i Γ ( 2 - c ) Γ ( c - b ) Γ ( a - b + 1 ) Γ ( 1 - a ) w 5 ( z ) , subscript 𝑤 2 𝑧 superscript 𝑒 1 𝑎 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑐 𝑏 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑐 𝑎 𝑏 1 subscript 𝑤 4 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑐 𝑏 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 1 𝑎 subscript 𝑤 5 𝑧 {\displaystyle{\displaystyle w_{2}(z)=e^{(1-a)\pi\mathrm{i}}\frac{\Gamma\left(% 2-c\right)\Gamma\left(c-b\right)}{\Gamma\left(a-c+1\right)\Gamma\left(c-a-b+1% \right)}w_{4}(z)+e^{-a\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-% b\right)}{\Gamma\left(a-b+1\right)\Gamma\left(1-a\right)}w_{5}(z),}}
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    DLMF:15.10.E35
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