Formula:794

Digital Library of Mathematical Functions ID 2.5.E48

${\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)\sim(-\ln\zeta)\sum_{k=0}^{\infty}\frac{\zeta^{k}}{k!}+\sum_{k=0}^{\infty}\psi\left(k+1\right)\frac{\zeta^{k}}{k!},}}$

Constraint(s)

${\displaystyle{\displaystyle\zeta\to 0+}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Laplace transform
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle h(x)}}$: locally integrable function
 

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