DLMF:5.12.E8 (Q2153)

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DLMF:5.12.E8
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ ∫ - ∞ ∞ d t ( w + i ⁢ t ) a ⁢ ( z - i ⁢ t ) b = ( w + z ) 1 - a - b ( a + b - 1 ) ⁢ B ⁡ ( a , b ) , 1 2 𝜋 superscript subscript 𝑡 superscript 𝑤 𝑖 𝑡 𝑎 superscript 𝑧 𝑖 𝑡 𝑏 superscript 𝑤 𝑧 1 𝑎 𝑏 𝑎 𝑏 1 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle{\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{% \mathrm{d}t}{(w+it)^{a}(z-it)^{b}}=\frac{(w+z)^{1-a-b}}{(a+b-1)\mathrm{B}\left% (a,b\right)}},}}
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    DLMF id
    DLMF:5.12.E8
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    constraint
    ℜ ⁡ ( a + b ) > 1 𝑎 𝑏 1 {\displaystyle{\displaystyle\Re(a+b)>1}}
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