Formula:793

Digital Library of Mathematical Functions ID 2.5.E47

${\displaystyle{\displaystyle\Residue_{z=1}\left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]=\left(-\ln\zeta-\gamma\right)-\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Residue}}$:
• ${\displaystyle{\displaystyle h(x)}}$: locally integrable function
 

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