DLMF:1.14.E37 (Q529)

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DLMF:1.14.E37
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    test
    ∫ 0 ∞ f ⁢ ( x ) ⁢ g ⁢ ( x ) ⁢ d x = 1 2 ⁢ π ⁢ i ⁢ ∫ σ - i ⁢ ∞ σ + i ⁢ ∞ ℳ ⁡ f ⁡ ( 1 - s ) ⁢ ℳ ⁡ g ⁡ ( s ) ⁢ d s . subscript superscript 0 𝑓 𝑥 𝑔 𝑥 𝑥 1 2 𝜋 𝑖 subscript superscript 𝜎 𝑖 𝜎 𝑖 Mellin-transform 𝑓 1 𝑠 Mellin-transform 𝑔 𝑠 𝑠 {\displaystyle{\displaystyle\int^{\infty}_{0}f(x)g(x)\mathrm{d}x=\frac{1}{2\pi i% }\*\int^{\sigma+i\infty}_{\sigma-i\infty}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu% \left(1-s\right)\mathscr{M}\mskip-3.0mu g\mskip 3.0mu \left(s\right)\mathrm{d% }s.}}
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    DLMF id
    DLMF:1.14.E37
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