used

mathbb：blackboard bold mathcal：calligraphy mathrm：math roman mathbf：math boldface

other

mathsf mathtt mathit widehat widetilde overline

illustration

\begin{equation}
\begin{aligned}
&F(x, y) = F(x) + F(y), \\
&\mathbb{F}(x, y) = \mathbb{F}(x) + \mathbb{F}(y), \\
&\mathcal{F}(x, y) = \mathcal{F}(x) + \mathcal{F}(y), \\
&\mathrm{F}(x, y) = \mathrm{F}(x) + \mathrm{F}(y), \\
&\mathbf{F}(x, y) = \mathbf{F}(x) + \mathbf{F}(y).
\end{aligned}
\end{equation}

\(F(x, y) = F(x) + F(y), \\ \mathbb{F}(x, y) = \mathbb{F}(x) + \mathbb{F}(y), \\ \mathcal{F}(x, y) = \mathcal{F}(x) + \mathcal{F}(y), \\ \mathrm{F}(x, y) = \mathrm{F}(x) + \mathrm{F}(y), \\ \mathbf{F}(x, y) = \mathbf{F}(x) + \mathbf{F}(y).\)