% For comparison with Euler Script and Ralph Smith's Formal Script
\usepackage[mathscr]{eucal} % \mathscr with Euler Script
\DeclareSymbolFont{rsfscript}{OMS}{rsfs}{m}{n}
\DeclareSymbolFontAlphabet{\mathrsfs}{rsfscript}
The script (calligraphic) math alphabet with Zapf Chancery
(\verb+\mathpzc+):
\[
\mathpzc{ABCDEFGHIJKLMNOPQRSTUVWXYZ\,
abcdefghijklmnopqrstuvwxyz\,
1234567890}
\]
The script (calligraphic) math alphabet with Euler Script
(\verb+\EuScript+):
\[
\EuScript{ABCDEFGHIJKLMNOPQRSTUVWXYZ\,abc\,123}
\]
The script (calligraphic) math alphabet with Ralph Smith's Formal Script
(\verb+\mathrsfs+):
\[
\mathrsfs{ABCDEFGHIJKLMNOPQRSTUVWXYZ\,abc\,123}
\]
The script (calligraphic) math alphabet with (\verb+\mathcal+):
\[
\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ\,abc\,123}
\]
The script (calligraphic) math alphabet with (\verb+\mathscr+):
\[
\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ\,abc\,123}
\]
Compare script letters (CM, CMcal, pzcm, EuScript, rsfs):
\[
H \CMcal{H} \mathpzc{H} \EuScript{H} \mathrsfs{H}
Z \CMcal{Z} \mathpzc{Z} \EuScript{Z} \mathrsfs{Z}
F \CMcal{F} \mathpzc{F} \EuScript{F} \mathrsfs{F}
\]
Usage examples with \verb+\mathcal+:
\[
\mathcal{F}\left\{ s(x)\right\} =\int_{-\infty}^{\infty}s(x)
\mathrm{e}^{\mathrm{i}\omega_{x}x}\,\mathrm{d}{x}
\]
Die Hamiltonfunktion ist die Legendre-Transformierte der Lagrange-Funktion
$\mathcal L(t,q,\dot q)$, die von den generalisierten Koordinaten und
ihren Geschwindigkeiten $\dot q=(\dot q_1,\dot q_2\dots \dot q_n)$ abhängt:
\[
\mathcal H(t,q,p)= \sum_{k=1}^n \dot q_k\, p_k - \mathcal L(t, q,\dot q)
\]
