DLMF:13.4.E17 (Q4380): Difference between revisions

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DLMF:13.4.E17
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = z - a 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( a + t ) ⁢ Γ ⁡ ( 1 + a - b + t ) ⁢ Γ ⁡ ( - t ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( 1 + a - b ) ⁢ z - t ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 2 𝜋 imaginary-unit superscript subscript imaginary-unit imaginary-unit Euler-Gamma 𝑎 𝑡 Euler-Gamma 1 𝑎 𝑏 𝑡 Euler-Gamma 𝑡 Euler-Gamma 𝑎 Euler-Gamma 1 𝑎 𝑏 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{-a}}{2\pi\mathrm{i}}% \int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(a+t\right)\Gamma% \left(1+a-b+t\right)\Gamma\left(-t\right)}{\Gamma\left(a\right)\Gamma\left(1+a% -b\right)}z^{-t}\mathrm{d}t,}}
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    DLMF id
    DLMF:13.4.E17
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