The only reference in my texts is Hill. I found this, but I suspect you already know what's in it.I am looking for either a paper or a book to show that Vector Spherical Harmonics form a complete set. I only need it for Euclidean 3 space. As I have been searching I have noticed that they are used in a lot in physics so If anyone has seen them in a mathematical physics book that would be awesome. I can seem to find many math books that talk about Spherical harmonics very much.

So far a I have used these references for Scalar Spherical Harmonics

Analysis of spherical symmetries in Euclidean spaces by Claus Muller

Pure and Applied mathematics vol IX orthogonal functions bu Sansone , G

and I have reference the standard Fourier analysis text by Stien and Wiess.

None of these really talk about Vector Spherical harmonics. However, I

I did find two journal articles in the Library

The Theory of Vector Spherical Harmonics , E.L Hill 1954 and

Vector spherical harmonics and their applications to magnetostatics, Barrera et al. 1984.

This 2nd paper claims that they are complete but does not supply the proof and a rundown of its references has not turned anything up.

Thanks

TES.

-Dan