Formula:501

Digital Library of Mathematical Functions ID 1.14.E40

${\displaystyle{\displaystyle\int^{\infty}_{0}x^{s-1}(f*g)(x)\mathrm{d}x=\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(s\right)\mathscr{M}\mskip-3.0mu g\mskip 3.0mu \left(s\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle*}}$: convolution (Mellin) (locally)
 

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