# 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) = 4πR^{2}φ(0).

(b)

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