Question: The spherical harmonics satisfy the relation: V6,4) Yim (0,0) = -1(1+1) Ylm (0,4). Yim (0', p')Ym (0, q) can be written on (a) Show

The spherical harmonics satisfy the relation: V6,4) Yim (0,0) = -1(1+1) Ylm

The spherical harmonics satisfy the relation: V6,4) Yim (0,0) = -1(1+1) Ylm (0,4). Yim (0', p')Ym (0, q) can be written on (a) Show that IP-P Etzo Em 4m=-1 41 21+1+ = Eizo Em=-127 (0(-1) where 8(x)) is the Heaviside function and 9(x) = 8(x). + 0(r-r'), ) Yim (0'. q')Ym (0, 4), (b) Prove that the result in part (a) is indeed satisfy the Poisson equation: 1 0 |7-7'| 8(r-r')8(0-0)8(p p') r sin 0 = -4n8(-7') = -4n-

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