DLMF:15.14.E1 (Q5176)

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DLMF:15.14.E1
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    Statements

    Defining formula
    ∫ 0 ∞ x s - 1 ⁢ 𝐅 ⁡ ( a , b c ; - x ) ⁢ d x = Γ ⁡ ( s ) ⁢ Γ ⁡ ( a - s ) ⁢ Γ ⁡ ( b - s ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) ⁢ Γ ⁡ ( c - s ) , superscript subscript 0 superscript 𝑥 𝑠 1 scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑥 𝑥 Euler-Gamma 𝑠 Euler-Gamma 𝑎 𝑠 Euler-Gamma 𝑏 𝑠 Euler-Gamma 𝑎 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑠 {\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c% };-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma% \left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s% \right)},}}
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    DLMF id
    DLMF:15.14.E1
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    constraint
    min ⁡ ( ℜ ⁡ a , ℜ ⁡ b ) > ℜ ⁡ s > 0 𝑎 𝑏 𝑠 0 {\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}
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