DLMF:15.10.E20 (Q5136)

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DLMF:15.10.E20
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    w 6 ( z ) = Γ ( 1 - c ) Γ ( b - a + 1 ) Γ ( b - c + 1 ) Γ ( 1 - a ) w 1 ( z ) + e ( c - 1 ) π i Γ ( c - 1 ) Γ ( b - a + 1 ) Γ ( b ) Γ ( c - a ) w 2 ( z ) . subscript 𝑤 6 𝑧 Euler-Gamma 1 𝑐 Euler-Gamma 𝑏 𝑎 1 Euler-Gamma 𝑏 𝑐 1 Euler-Gamma 1 𝑎 subscript 𝑤 1 𝑧 superscript 𝑒 𝑐 1 𝜋 imaginary-unit Euler-Gamma 𝑐 1 Euler-Gamma 𝑏 𝑎 1 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑎 subscript 𝑤 2 𝑧 {\displaystyle{\displaystyle w_{6}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(% b-a+1\right)}{\Gamma\left(b-c+1\right)\Gamma\left(1-a\right)}w_{1}(z)+e^{(c-1)% \pi\mathrm{i}}\frac{\Gamma\left(c-1\right)\Gamma\left(b-a+1\right)}{\Gamma% \left(b\right)\Gamma\left(c-a\right)}w_{2}(z).}}
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