DLMF:1.14.E40 (Q532)

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DLMF:1.14.E40
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    Statements

    Defining formula
    ∫ 0 ∞ x s - 1 ⁢ ( f * g ) ⁢ ( x ) ⁢ d x = ℳ ⁡ f ⁡ ( s ) ⁢ ℳ ⁡ 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).}}
    0 references
    DLMF id
    DLMF:1.14.E40
    0 references
    Symbols used
    Mellin transform
    Defining formula
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2agdec
    0 references
     
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