Formula:752

Digital Library of Mathematical Functions ID 2.5.E6

${\displaystyle{\displaystyle I(x)=\sum\limits_{d<\Re z<c}\Residue\left[x^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)\right]+E(x),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\Residue}}$:
• ${\displaystyle{\displaystyle f(x)}}$: locally integrable function
• ${\displaystyle{\displaystyle c}}$: point
• ${\displaystyle{\displaystyle I(x)}}$: convolution integral
• ${\displaystyle{\displaystyle h(x)}}$: function
• ${\displaystyle{\displaystyle d}}$: point
• ${\displaystyle{\displaystyle E(x)}}$: function
 

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