DLMF:15.10.E25 (Q5141)

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DLMF:15.10.E25
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    Statements

    Defining formula
    w 1 ⁢ ( z ) = Γ ⁡ ( c ) ⁢ Γ ⁡ ( b - a ) Γ ⁡ ( b ) ⁢ Γ ⁡ ( c - a ) ⁢ w 5 ⁢ ( z ) + Γ ⁡ ( c ) ⁢ Γ ⁡ ( a - b ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( c - b ) ⁢ w 6 ⁢ ( z ) , subscript 𝑤 1 𝑧 Euler-Gamma 𝑐 Euler-Gamma 𝑏 𝑎 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑎 subscript 𝑤 5 𝑧 Euler-Gamma 𝑐 Euler-Gamma 𝑎 𝑏 Euler-Gamma 𝑎 Euler-Gamma 𝑐 𝑏 subscript 𝑤 6 𝑧 {\displaystyle{\displaystyle w_{1}(z)=\frac{\Gamma\left(c\right)\Gamma\left(b-% a\right)}{\Gamma\left(b\right)\Gamma\left(c-a\right)}w_{5}(z)+\frac{\Gamma% \left(c\right)\Gamma\left(a-b\right)}{\Gamma\left(a\right)\Gamma\left(c-b% \right)}w_{6}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E25
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1xdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1xdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1xdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1udec
    0 references
    Q11667
    Defining formula
    w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}
    xml-id
    C15.S10.XMD2.m1ndec
    0 references
     
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