Script l (ℓ) in LaTeX
\ell produces ℓ, a script lowercase l used wherever a plain italic l would be hard to tell apart from the digit 1 or the letter I, and conventionally for lengths, indices and the ell-p sequence spaces.
LaTeX command
\ellNot the symbol you meant? Draw it to find the command →
The main reason \ell exists is legibility: in most maths fonts, an italic lowercase l is nearly indistinguishable from the digit 1, and sometimes from a capital I. \ell's cursive form removes that ambiguity, which matters especially when converting handwritten notes, where the same confusion is common on the page.
Its best-known use is naming sequence spaces in functional analysis: \ell^2 is the space of square-summable sequences, \ell^\infty the space of bounded sequences, and \ell^p the general family for . These are standard, fixed names, always written with \ell rather than a plain l.
It also appears as a physical length or arc-length variable, as a generic index or counter, and in physics as the orbital angular momentum quantum number, where it is again preferred over l for exactly the same readability reason.
Examples
$\ell^2$the space of square-summable sequences
$\ell^{\infty}$the space of bounded sequences
$\sum_{n=1}^{\infty} |x_n|^2 < \infty \iff x \in \ell^2$the defining condition for membership in ell-2
Tips and common mistakes
- Use
\ellwhenever a lowercase l risks being read as 1 or I, this is a frequent source of transcription errors from handwritten maths. \ell^2,\ell^pand\ell^\infty are the fixed, standard names for sequence spaces in analysis; don't substitute a plain letter l in these.- In quantum mechanics,
\elldenotes the orbital angular momentum quantum number, kept distinct from L (total angular momentum). - No package is required;
\ellis available in core LaTeX and KaTeX.
Working from handwritten notes?
LatexNotes turns a photo or PDF of handwritten mathematics into clean, compilable LaTeX - graphs and all. Free to try, no sign-up.
Convert your maths to LaTeX →FAQ
What is \ell used for in LaTeX?
A script lowercase l, used wherever a plain l would be confused with 1 or I, and conventionally for lengths, indices, and the ell-p sequence spaces.
What is \ell^2 space?
The space of square-summable sequences, a fundamental example of a Hilbert space in functional analysis, written \ell^2.
Is \ell the same letter as l?
They represent the same lowercase L, just drawn with a distinct cursive glyph for clarity; the underlying meaning is identical.
Does \ell need a package?
No, it is available in core LaTeX and KaTeX with no extra package required.