TeXipedia

ell

Represents a script lowercase L commonly used in mathematical notation to denote various quantities or parameters.

Overview

Widely used across mathematics and physics to represent specific variables or quantities, particularly when a standard 'l' might be confused with the number '1' or capital 'I'.

  • Common in linear algebra to denote linear functions or mappings
  • Frequently appears in number theory for length parameters
  • Used in physics to represent angular momentum
  • Popular in probability theory and statistics for likelihood functions
  • Often employed when defining sequences or indexing variables

Examples

Representing angular momentum in physics equations.

L=mr2ω=r×p=ℓℏL = mr^2\omega = r \times p = \ell \hbar 
L = mr^2\omega = r \times p = \ell \hbar

Denoting a generic length parameter in mathematical expressions.

f(ℓ)=∫0ℓx2 dxf(\ell) = \int_0^{\ell} x^2 \, dx 
f(\ell) = \int_0^{\ell} x^2 \, dx

Indicating the ℓ-th term in a sequence or series.

aℓ=1ℓ2for ℓ≥1a_\ell = \frac{1}{\ell^2} \quad \text{for } \ell \geq 1 
a_\ell = \frac{1}{\ell^2} \quad \text{for } \ell \geq 1