DLMF:15.10.E24 (Q5140)

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DLMF:15.10.E24
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    Statements

    test
    w 6 ⁢ ( z ) = e b ⁢ π ⁢ i ⁢ Γ ⁡ ( b - a + 1 ) ⁢ Γ ⁡ ( c - a - b ) Γ ⁡ ( 1 - a ) ⁢ Γ ⁡ ( c - a ) ⁢ w 3 ⁢ ( z ) + e ( c - a ) ⁢ π ⁢ i ⁢ Γ ⁡ ( b - a + 1 ) ⁢ Γ ⁡ ( a + b - c ) Γ ⁡ ( b ) ⁢ Γ ⁡ ( b - c + 1 ) ⁢ w 4 ⁢ ( z ) . subscript 𝑤 6 𝑧 superscript 𝑒 𝑏 𝜋 imaginary-unit Euler-Gamma 𝑏 𝑎 1 Euler-Gamma 𝑐 𝑎 𝑏 Euler-Gamma 1 𝑎 Euler-Gamma 𝑐 𝑎 subscript 𝑤 3 𝑧 superscript 𝑒 𝑐 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑏 𝑎 1 Euler-Gamma 𝑎 𝑏 𝑐 Euler-Gamma 𝑏 Euler-Gamma 𝑏 𝑐 1 subscript 𝑤 4 𝑧 {\displaystyle{\displaystyle w_{6}(z)=e^{b\pi\mathrm{i}}\frac{\Gamma\left(b-a+% 1\right)\Gamma\left(c-a-b\right)}{\Gamma\left(1-a\right)\Gamma\left(c-a\right)% }w_{3}(z)+e^{(c-a)\pi\mathrm{i}}\frac{\Gamma\left(b-a+1\right)\Gamma\left(a+b-% c\right)}{\Gamma\left(b\right)\Gamma\left(b-c+1\right)}w_{4}(z).}}
    0 references
    DLMF id
    DLMF:15.10.E24
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
     
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