DLMF:15.10.E26 (Q5142)

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DLMF:15.10.E26
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    Statements

    test
    w 2 ⁢ ( z ) = e ( 1 - c ) ⁢ π ⁢ i ⁢ Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( b - a ) Γ ⁡ ( 1 - a ) ⁢ Γ ⁡ ( b - c + 1 ) ⁢ w 5 ⁢ ( z ) + e ( 1 - c ) ⁢ π ⁢ i ⁢ Γ ⁡ ( 2 - c ) ⁢ Γ ⁡ ( a - b ) Γ ⁡ ( 1 - b ) ⁢ Γ ⁡ ( a - c + 1 ) ⁢ w 6 ⁢ ( z ) , subscript 𝑤 2 𝑧 superscript 𝑒 1 𝑐 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑏 𝑎 Euler-Gamma 1 𝑎 Euler-Gamma 𝑏 𝑐 1 subscript 𝑤 5 𝑧 superscript 𝑒 1 𝑐 𝜋 imaginary-unit Euler-Gamma 2 𝑐 Euler-Gamma 𝑎 𝑏 Euler-Gamma 1 𝑏 Euler-Gamma 𝑎 𝑐 1 subscript 𝑤 6 𝑧 {\displaystyle{\displaystyle w_{2}(z)=e^{(1-c)\pi\mathrm{i}}\frac{\Gamma\left(% 2-c\right)\Gamma\left(b-a\right)}{\Gamma\left(1-a\right)\Gamma\left(b-c+1% \right)}w_{5}(z)+e^{(1-c)\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left% (a-b\right)}{\Gamma\left(1-b\right)\Gamma\left(a-c+1\right)}w_{6}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E26
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1ydec
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    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ydec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1ydec
    0 references
     
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