Use the orthogonality properties of the spherical harmonics to prove the following identities for a function (r) which satisfies Laplaces equation in and on an origin-centered spherical surface S of radius R: (a) dS (r) = 4R 2 (0). (b) I S dSzo(r) = = 3 R4 z r=0
Chapter 7, Problems #1
Use the orthogonality properties of the spherical harmonics to prove the following identities for a function φ(r) which satisfies Laplace’s equation in and on an origin-centered spherical surface S of radius R:
(a) ∫ dS φ(r) = 4πR2φ(0).
(b)
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