DLMF:15.6.E8 (Q5046)

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DLMF:15.6.E8
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b ; c ; z ) = 1 Γ ⁡ ( c - d ) ⁢ ∫ 0 1 𝐅 ⁡ ( a , b ; d ; z ⁢ t ) ⁢ t d - 1 ⁢ ( 1 - t ) c - d - 1 ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 1 Euler-Gamma 𝑐 𝑑 superscript subscript 0 1 scaled-hypergeometric-bold-F 𝑎 𝑏 𝑑 𝑧 𝑡 superscript 𝑡 𝑑 1 superscript 1 𝑡 𝑐 𝑑 1 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\frac{1}{\Gamma% \left(c-d\right)}\int_{0}^{1}\mathbf{F}\left(a,b;d;zt\right)t^{d-1}(1-t)^{c-d-% 1}\mathrm{d}t,}}
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    DLMF id
    DLMF:15.6.E8
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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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