DLMF:15.10.E31 (Q5147)

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DLMF:15.10.E31
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    Statements

    test
    w 2 ⁢ ( z ) = e ( b - c + 1 ) ⁢ π ⁢ i ⁢ Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( a ) Γ ⁡ ( a + b - c + 1 ) ⁢ Γ ⁡ ( 1 - b ) ⁢ w 3 ⁢ ( z ) + e ( b - c ) ⁢ π ⁢ i ⁢ Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( a ) Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( b - c + 1 ) ⁢ w 5 ⁢ ( z ) , subscript 𝑤 2 𝑧 superscript 𝑒 𝑏 𝑐 1 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 𝑐 1 Euler-Gamma 1 𝑏 subscript 𝑤 3 𝑧 superscript 𝑒 𝑏 𝑐 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑏 𝑐 1 subscript 𝑤 5 𝑧 {\displaystyle{\displaystyle w_{2}(z)=e^{(b-c+1)\pi\mathrm{i}}\frac{\Gamma% \left(2-c\right)\Gamma\left(a\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(1-% b\right)}w_{3}(z)+e^{(b-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma% \left(a\right)}{\Gamma\left(a-b+1\right)\Gamma\left(b-c+1\right)}w_{5}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E31
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2andec
    0 references
     
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