Formula:790

Digital Library of Mathematical Functions ID 2.5.E44

${\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta\right)\sim\sum_{n=0}^{\infty}b_{n}\Gamma\left(1-\beta_{n}\right)\zeta^{\beta_{n}-1}+\sum\limits_{n=0}^{\infty}\frac{(-\zeta)^{n}}{n!}\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(n+1\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Laplace transform
• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle h(x)}}$: locally integrable function
• ${\displaystyle{\displaystyle b}}$: right endpoint
 

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