DLMF:15.10.E22 (Q5138)

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DLMF:15.10.E22
No description defined

    Statements

    Defining formula
    w 2 ⁢ ( z ) = Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( c - a - b ) Γ ⁡ ( 1 - a ) ⁢ Γ ⁡ ( 1 - b ) ⁢ w 3 ⁢ ( z ) + Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( a + b - c ) Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( b - c + 1 ) ⁢ w 4 ⁢ ( z ) , subscript 𝑤 2 𝑧 Euler-Gamma 2 𝑐 Euler-Gamma 𝑐 𝑎 𝑏 Euler-Gamma 1 𝑎 Euler-Gamma 1 𝑏 subscript 𝑤 3 𝑧 Euler-Gamma 2 𝑐 Euler-Gamma 𝑎 𝑏 𝑐 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑏 𝑐 1 subscript 𝑤 4 𝑧 {\displaystyle{\displaystyle w_{2}(z)=\frac{\Gamma\left(2-c\right)\Gamma\left(% c-a-b\right)}{\Gamma\left(1-a\right)\Gamma\left(1-b\right)}w_{3}(z)+\frac{% \Gamma\left(2-c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a-c+1\right)\Gamma% \left(b-c+1\right)}w_{4}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E22
    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.m2aedec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1udec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1udec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1udec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1rdec
    0 references
    Q11667
    Defining formula
    w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}
    xml-id
    C15.S10.XMD2.m1kdec
    0 references
     
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