DLMF:18.19.E7 (Q5837)

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DLMF:18.19.E7
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    w ( λ ) ( z ; ϕ ) = Γ ( λ + i z ) Γ ( λ - i z ) e ( 2 ϕ - π ) z , superscript 𝑤 𝜆 𝑧 italic-ϕ Euler-Gamma 𝜆 𝑖 𝑧 Euler-Gamma 𝜆 𝑖 𝑧 superscript 𝑒 2 italic-ϕ 𝜋 𝑧 {\displaystyle{\displaystyle w^{(\lambda)}(z;\phi)=\Gamma\left(\lambda+iz% \right)\Gamma\left(\lambda-iz\right)e^{(2\phi-\pi)z},}}
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    DLMF:18.19.E7
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
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    w ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    C18.S1.XMD10.m1bdec
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