DLMF:1.14.E40 (Q532)

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DLMF:1.14.E40
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    0 x s - 1 ( f * g ) ( x ) d x = f ( s ) g ( s ) . subscript superscript 0 superscript 𝑥 𝑠 1 𝑓 𝑔 𝑥 𝑥 Mellin-transform 𝑓 𝑠 Mellin-transform 𝑔 𝑠 {\displaystyle{\displaystyle\int^{\infty}_{0}x^{s-1}(f*g)(x)\mathrm{d}x=% \mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)\mathscr{M}\mskip-3.0mu g% \mskip 3.0mu \left(s\right).}}
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    DLMF:1.14.E40
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    ( f ) ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E32.m2agdec
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