DLMF:15.6.E1 (Q5039)

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DLMF:15.6.E1
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b ; c ; z ) = 1 Γ ⁡ ( b ) ⁢ Γ ⁡ ( c - b ) ⁢ ∫ 0 1 t b - 1 ⁢ ( 1 - t ) c - b - 1 ( 1 - z ⁢ t ) a ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 1 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑏 superscript subscript 0 1 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)=\frac{1}{\Gamma% \left(b\right)\Gamma\left(c-b\right)}\int_{0}^{1}\frac{t^{b-1}(1-t)^{c-b-1}}{(% 1-zt)^{a}}\mathrm{d}t,}}
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    DLMF id
    DLMF:15.6.E1
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    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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