DLMF:15.6.E4 (Q5042)

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DLMF:15.6.E4
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b ; c ; z ) = e - b ⁢ π ⁢ i ⁢ Γ ⁡ ( 1 - b ) 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( c - b ) ⁢ ∫ 1 ( 0 + ) t b - 1 ⁢ ( 1 - t ) c - b - 1 ( 1 - z ⁢ t ) a ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 superscript 𝑒 𝑏 𝜋 imaginary-unit Euler-Gamma 1 𝑏 2 𝜋 imaginary-unit Euler-Gamma 𝑐 𝑏 superscript subscript 1 limit-from 0 superscript 𝑡 𝑏 1 superscript 1 𝑡 𝑐 𝑏 1 superscript 1 𝑧 𝑡 𝑎 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=e^{-b\pi\mathrm{i}}% \frac{\Gamma\left(1-b\right)}{2\pi\mathrm{i}\Gamma\left(c-b\right)}\int_{1}^{(% 0+)}\frac{t^{b-1}(1-t)^{c-b-1}}{(1-zt)^{a}}\mathrm{d}t,}}
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    DLMF id
    DLMF:15.6.E4
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