.png&w=64&q=75){kind=small}
Integral transforms use calligraphic capitals: \mathcal{L} for Laplace, \mathcal{F} for Fourier, \mathcal{Z} for the Z-transform. \mathcal is built into KaTeX; the fancier \mathscr needs mathrsfs in LaTeX and is not available in most web renderers.
All ways to write it
| Command | Use | Package | Copy |
|---|---|---|---|
\mathcal{L}\{f(t)\} | calligraphic L | none | |
\mathcal{L}^{-1} | inverse transform | none | |
\mathscr{L} | script L | mathrsfsnot in KaTeX | |
\mathcal{F} | Fourier transform | none |
Commands marked with a package need that \usepackage line in a LaTeX document. “Not in KaTeX” means the command will not render in KaTeX- or MathJax-based tools such as Markdown previews, Jupyter and Confluence math apps; use one of the other forms there.
Example
\mathcal{L}\{e^{at}\}(s) = \frac{1}{s - a}, \quad s > aThe Laplace transform of an exponential.
Questions
How do I get curly braces around the function?
Braces are special characters, so escape them: \{ f(t) \}. For scaling braces use \left\{ and \right\}.
Related symbols
- Laplacian ∆
\Delta - Integral ∫
\int_{a}^{b} f(x)\,dx
Using laplace transform in Confluence
Confluence Cloud has no built-in LaTeX. With LaTeX Math for Confluence you add a math macro to any page, type \mathcal{L}\{f(t)\} and it renders inline or as a block, with a live preview while you edit. The app uses KaTeX, so pick one of the commands above that is not marked “not in KaTeX”.