Formula:751

Digital Library of Mathematical Functions ID 2.5.E5

${\displaystyle{\displaystyle I(x)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}x^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)\mathrm{d}z,}}$

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
• ${\displaystyle{\displaystyle f(x)}}$: locally integrable function
• ${\displaystyle{\displaystyle c}}$: point
• ${\displaystyle{\displaystyle I(x)}}$: convolution integral
• ${\displaystyle{\displaystyle h(x)}}$: function
 

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