Question

Sphrical harmonic as imp It is defined as Ye" (0,0) YE (014) -1) [+T (Cm) Also x" (0-4)=-4-1)" ye^(0-0) Wil prave Hende tietto ore 10-4-47 (2007 Presscom fortlat-6' [ 2# coeloszt (eo) 7² p (cas) e 26/2 wee IT Ý Conte ' [241. P (Casco da " Pitesores k (x) = (1-x²)²2 I left P. ( v ol. ² is tocar لنکس (هم)) (هر،)PA coro). Le since P (rose) ti (oso) - b (case) 3 as a sing zsin'd ₂ (sin o 1) sin -Prove that cord) = 1 / y (0-0) = ( 3 Cos² 0 - 2) sino coso ei

Answer 1

2 Spherical Harmonics : Y 19,0) = (Ql+1) (lm)! po trosed into where P(x) = (-1) (1-x2) m/2 d Ctm (2²-De gleda daerm From list of Legendre polynomials: Po (x) = 3 x²-1 & ph / (x) - - 3x (1-x2)% so Po (coso) = 3c05²0-1 & P 1 (coso) =-3sinowso 2 Ibus You (0,4)= 1 5 21 po (coso) o (4) = (360520-1) = F (Boosto-1) Ee Ye (o_d) =(-) 62 (0,4))* on t (-3650 sino) e') = (a brososîne) ep) (Bosebine) e't. 247