Formula:497

Digital Library of Mathematical Functions ID 1.14.E36

${\displaystyle{\displaystyle\int^{\infty}_{0}f(x)g(yx)\mathrm{d}x=\frac{1}{2\pi i}\*\int^{\sigma+i\infty}_{\sigma-i\infty}y^{-s}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-s\right)\mathscr{M}\mskip-3.0mu g\mskip 3.0mu \left(s\right)\mathrm{d}s,}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sigma\in(a,b)}}$: parameter
 

Resources that cite this formula

No records found.