4) 5) Show that Y Find Ye Find Y 7 - Do this imo Y(0,0) (21+1)(1-1)! 488 (2+m)! ep₁ (case) Y's (0,0) = (2(3)+1)(3-6-3)!

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4 5 Show That Y Find Ye Find Y 7 Do This Imo Y 0 0 21 1 1 1 488 2 M Ep Case Y S 0 0 2 3 1 3 6 3 1 (98.14 KiB) Viewed 40 times

4) 5) Show that Y Find Ye Find Y 7 - Do this imo Y(0,0) (21+1)(1-1)! 488 (2+m)! ep₁ (case) Y's (0,0) = (2(3)+1)(3-6-3)! ep (cos8) 41 (3+(-3))! Y -5; 9 e = P₂ (COSA) (7)(6)! 47 then find P₁ PX(X) P So P. GO (+2²5) (-1) (3-3)! P} (x) (313)! = -1 (-1)² (₁-x²) ² α ³² (x²p³ 3+3 dx d' (x²13³= d² (x²-1-3x² + 3x ²)! dxu dxº (1-x²) 3(x) = -16-17 61-8.5! 47 plug x = cose P₂ (COSA) + 1 (1-(05²0) } 48 P²₁ ((050) =1 42 P (case) + sine 48 # -SY then subtitute in Y`'s (0,4)= 7-720 e *Sin³0 48 -314 Y(0,4)=0.417 C sine # Normalization sine de dedo [19² +² Sindar de fin ²² d. 1 10² YI'sin edede- IRI+²dr =1 $ ### √** Sº 8.0 8-1 The normalize angular vare function is called spherical harmonies Y (8,00) (2841)(1-1)! ep (cosa) 4 (d+n)! → 1 m² do 1
4) Show that Y -m e = m (-1) (Y) m e