An Etymological Dictionary of Astronomy and Astrophysics

A variable used in → spherical harmonic expansions. Each spherical harmonic is characterized by its multipole index l: l = 0 for a → monopole, l = 1 for a → dipole, and so on. It is used in particular to describe the
→ cosmic microwave background anisotropy:

ΔT/T₀ (θ,φ) = Σ a_lmY_lm(θ,φ), where θ and φ are the → spherical polar coordinates, Y_lm is the → spherical harmonic functions, and the sum runs over l = 1, 2, …, ∞ and m = -l, …, l, where the multipole index l corresponds to angular scales ≅ 180°/l.

See also: → multipole; → index.