DLMF:15.10.E18 (Q5134)

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DLMF:15.10.E18
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    Statements

    Defining formula
    w 4 ⁢ ( z ) = Γ ⁡ ( 1 - c ) ⁢ Γ ⁡ ( c - a - b + 1 ) Γ ⁡ ( 1 - a ) ⁢ Γ ⁡ ( 1 - b ) ⁢ w 1 ⁢ ( z ) + Γ ⁡ ( c - 1 ) ⁢ Γ ⁡ ( c - a - b + 1 ) Γ ⁡ ( c - a ) ⁢ Γ ⁡ ( c - b ) ⁢ w 2 ⁢ ( z ) , subscript 𝑤 4 𝑧 Euler-Gamma 1 𝑐 Euler-Gamma 𝑐 𝑎 𝑏 1 Euler-Gamma 1 𝑎 Euler-Gamma 1 𝑏 subscript 𝑤 1 𝑧 Euler-Gamma 𝑐 1 Euler-Gamma 𝑐 𝑎 𝑏 1 Euler-Gamma 𝑐 𝑎 Euler-Gamma 𝑐 𝑏 subscript 𝑤 2 𝑧 {\displaystyle{\displaystyle w_{4}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(% c-a-b+1\right)}{\Gamma\left(1-a\right)\Gamma\left(1-b\right)}w_{1}(z)+\frac{% \Gamma\left(c-1\right)\Gamma\left(c-a-b+1\right)}{\Gamma\left(c-a\right)\Gamma% \left(c-b\right)}w_{2}(z),}}
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    DLMF id
    DLMF:15.10.E18
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