Update: I’m Still Active, the Math is Just Tricky

Joseph Mellor
5 min readFeb 24, 2024

I’m just writing this article to let you know I’m still writing and to explain my future plans.

As a quick summary, I’m still writing articles, but

  • it’s just taking more time because the articles are getting more difficult and technical to write,
  • I have less free time to write articles,
  • and my mostly-written articles are several articles in the future.

I’ll also open up other things like a Patreon and a Substack some point in the future.

Multipole Expansion

Standard textbooks like Griffiths, Purcell, Jackson, ect. don’t have derivations for the multipole expansion. While I have dealt with this problem many times (e.g. Spherical Harmonics, Lagrangian Mechanics, Differential Forms, Lagrangian Field Theory in an article I don’t have out yet, etc.), it’s particularly difficult here for a few main reasons.

  • I don’t know how to use any computer algebra system for this problem since I have very specific requirements on the expansion.
  • People rarely list terms higher than the quadrupole moment, so I can’t check my work for the higher-order moments, which is a double whammy because the higher-order moments are where problems in derivations can appear.



Joseph Mellor

BS in Physics, Math, and CS with a minor in High-Performance Computing. You can find all my articles at https://josephmellor.xyz/articles/.