alkaline wrote:(L)[sup]2[/sup] = 2/r*d/dr + (d/dr)[sup]2[/sup] + cosθ/sinθ*d/dθ + 1/r[sup]2[/sup]*(d/dθ)[sup]2[/sup] + 1/r[sup]2[/sup]sin[sup]2[/sup]θ*(d/dφ)[sup]2[/sup]
I don't know why Eric Weisstein put it into the form shown in:
http://mathworld.wolfram.com/Laplacian.html
a quick further derivation of that version shows you are probably correct with the above "quoted version"
A further look though, derivation of wolframs third term your third term looks more like: [1/(r[sup]2[/sup]tan(θ))] δ/δθ (so you missed deviding by r[sup]2[/sup])
the rest of your terms I could reobtain from Eric's more compact version!
I don't know though whether it is correct to write δ[sup]2[/sup]/δθ[sup]2[/sup] as (δ/δθ)[sup]2[/sup]
Boy you have me reaquainting with stuff I have forgotten while back
, It'l take me a while to understand these things enough to figure the glomar laplacian, or perhaps the more general n-spherical.
I thought the upsidedown delta was called nabla but that doesn't seem to be recognized