If you have a function f(x), you can decompose it as an infinite sum of sine waves of the form sin(nx) and cos(nx) for increasing n. If you have a function g(theta,phi), you can decompose it into spherical harmonics; for each order l you have 2l+1 spherical harmonics. Is there anything special about this fact, that for nth order behavior of f(x) you only need 2 functions for each step (sin and cos), but for lth order behavior of g(theta,phi) you need 2l+1 functions?//<![CDATA[ aax_getad_mpb({ "slot_uuid":"f485bc30-20f5-4c34-b261-5f2d6f6142cb" }); //]]>

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spherical harmonic decomposition

Have something to add?

**Physics Forums - The Fusion of Science and Community**