DLMF:15.10.E17 (Q5133)

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DLMF:15.10.E17
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    Statements

    test
    w 3 ⁢ ( z ) = Γ ⁡ ( 1 - c ) ⁢ Γ ⁡ ( a + b - c + 1 ) Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( b - c + 1 ) ⁢ w 1 ⁢ ( z ) + Γ ⁡ ( c - 1 ) ⁢ Γ ⁡ ( a + b - c + 1 ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) ⁢ w 2 ⁢ ( z ) , subscript 𝑤 3 𝑧 Euler-Gamma 1 𝑐 Euler-Gamma 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑏 𝑐 1 subscript 𝑤 1 𝑧 Euler-Gamma 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 Euler-Gamma 𝑏 subscript 𝑤 2 𝑧 {\displaystyle{\displaystyle w_{3}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(% a+b-c+1\right)}{\Gamma\left(a-c+1\right)\Gamma\left(b-c+1\right)}w_{1}(z)+% \frac{\Gamma\left(c-1\right)\Gamma\left(a+b-c+1\right)}{\Gamma\left(a\right)% \Gamma\left(b\right)}w_{2}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E17
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1pdec
    0 references
    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1pdec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1pdec
    0 references
    Q11647
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1mdec
    0 references
     
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