Formula:481

Digital Library of Mathematical Functions ID 1.14.E20

${\displaystyle{\displaystyle f(t)=\frac{1}{2\pi i}\lim_{T\to\infty}\int^{\sigma+iT}_{\sigma-iT}e^{ts}\mathscr{L}\mskip-3.0mu f\mskip 3.0mu \left(s\right)\mathrm{d}s,}}$

Constraint(s)

${\displaystyle{\displaystyle\sigma>\alpha}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Laplace transform
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sigma\in(a,b)}}$: parameter
• ${\displaystyle{\displaystyle\alpha}}$: constant
 

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