TeXipedia

mathscr

Provides decorative script-style mathematical letters, commonly used for special mathematical sets and operators in formal notation.

Overview

Creates elegant, calligraphic-style characters particularly valued in mathematical writing for distinguishing special sets, operators, and mathematical constructs from regular variables.

  • Popular in advanced mathematics for denoting function spaces, algebras, and special collections
  • Often used to represent Hilbert spaces, Fourier transforms, and other mathematical objects requiring distinct notation
  • Requires the mathrsfs package for full functionality
  • Primarily works with uppercase letters, though some implementations support lowercase and numbers

Examples

Using script letters to denote special mathematical sets or spaces.

L:RR\mathscr{L} : \mathbb{R} \to \mathbb{R}
\mathscr{L} : \mathbb{R} \to \mathbb{R}

Representing a collection or family of sets in set theory.

F={A1,A2,,An}\mathscr{F} = \{A_1, A_2, \ldots, A_n\}
\mathscr{F} = \{A_1, A_2, \ldots, A_n\}

Denoting a mathematical operator or transform.

Hf(x)=f(t)xtdt\mathscr{H}f(x) = \int_{-\infty}^{\infty} \frac{f(t)}{x-t}\,dt
\mathscr{H}f(x) = \int_{-\infty}^{\infty} \frac{f(t)}{x-t}\,dt