DLMF:13.4.E18 (Q4381)

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DLMF:13.4.E18
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    Statements

    test
    U ⁡ ( a , b , z ) = z 1 - b ⁢ e z 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( b - 1 + t ) ⁢ Γ ⁡ ( t ) Γ ⁡ ( a + t ) ⁢ z - t ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 1 𝑏 superscript 𝑒 𝑧 2 𝜋 imaginary-unit superscript subscript imaginary-unit imaginary-unit Euler-Gamma 𝑏 1 𝑡 Euler-Gamma 𝑡 Euler-Gamma 𝑎 𝑡 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{1-b}e^{z}}{2\pi% \mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(b-1+t% \right)\Gamma\left(t\right)}{\Gamma\left(a+t\right)}z^{-t}\mathrm{d}t,}}
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    DLMF id
    DLMF:13.4.E18
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