Editing Laplace transform (section)

=== Bilateral Laplace transform ===
{{Main article|Two-sided Laplace transform}}

When one says "the Laplace transform" without qualification, the unilateral or one-sided transform is usually intended. The Laplace transform can be alternatively defined as the ''bilateral Laplace transform'', or [[two-sided Laplace transform]], by extending the limits of integration to be the entire real axis. If that is done, the common unilateral transform simply becomes a special case of the bilateral transform, where the definition of the function being transformed is multiplied by the [[Heaviside step function]].

The bilateral Laplace transform {{math|''F''(''s'')}} is defined as follows:
{{Equation box 1
|indent = :
|equation = <math>F(s) = \int_{-\infty}^\infty e^{-st} f(t)\, dt.</math>
|ref = Eq. 2
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|border colour = #0073CF
|background colour=#F5FFFA}}
An alternate notation for the bilateral Laplace transform is <math>\mathcal{B}\{f\}</math>, instead of {{mvar|F}}.