DLMF:13.4.E14 (Q4377)

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DLMF:13.4.E14
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    Statements

    test
    U ⁡ ( a , b , z ) = e - a ⁢ π ⁢ i ⁢ Γ ⁡ ( 1 - a ) 2 ⁢ π ⁢ i ⁢ ∫ ∞ ( 0 + ) e - z ⁢ t ⁢ t a - 1 ⁢ ( 1 + t ) b - a - 1 ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 1 𝑎 2 𝜋 imaginary-unit superscript subscript limit-from 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 𝑎 1 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=e^{-a\pi\mathrm{i}}\frac{% \Gamma\left(1-a\right)}{2\pi\mathrm{i}}\int_{\infty}^{(0+)}e^{-zt}t^{a-1}{(1+t% )^{b-a-1}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E14
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\frac{1}{2}\pi}}
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