Question these 2 questions are related. i included legendres solution 9. Show that if we let x = cos 6, the solution of the associated Legendre's equation (Equa. tion (7-47)] is y = cos 0 when l = 1 and m = O and is y = sin & when l = 1 and m = 1. 10. Show that if we let x = cos 0, the solution of the associated Legendre's equation [Equa- tion (7-47)] is y = {(3 cos? 0 - 1), when l = 2 and m = 0. ) 2 0. = dm y = (1 - x2)m/2. (7-47) dxm Pe(x)
IZD9FK The Asker · Calculus
these 2 questions are related. i included legendres solution
Transcribed Image Text: 9. Show that if we let x = cos 6, the solution of the associated Legendre's equation (Equa. tion (7-47)] is y = cos 0 when l = 1 and m = O and is y = sin & when l = 1 and m = 1. 10. Show that if we let x = cos 0, the solution of the associated Legendre's equation [Equa- tion (7-47)] is y = {(3 cos? 0 - 1), when l = 2 and m = 0. ) 2 0. =
dm y = (1 - x2)m/2. (7-47) dxm Pe(x)
More Transcribed Image Text: 9. Show that if we let x = cos 6, the solution of the associated Legendre's equation (Equa. tion (7-47)] is y = cos 0 when l = 1 and m = O and is y = sin & when l = 1 and m = 1. 10. Show that if we let x = cos 0, the solution of the associated Legendre's equation [Equa- tion (7-47)] is y = {(3 cos? 0 - 1), when l = 2 and m = 0. ) 2 0. =
dm y = (1 - x2)m/2. (7-47) dxm Pe(x)
Community Answer
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y=(1-x^(2))^(m//2)(d^(m))/(dx^(m))P_(l)(x)The n^("th ") Legendre polynomial,{:[P_(n)(x)=(1)/(2^(n)n!)(d^(n))/(dx^(n))(x^(2)-1)^(n)],[:.P_(1)(x)=(1)/(2xx1)(d)/(dx)(x^(2)-1)=(2x)/(2)=x],[P_(2)(x)=(1)/(2^(2)xx2!)(d^(2))/(dx^(2))(x^(2)-1)^(2)],[=(1)/(8)(d)/(dx)(2(x^(2)-1)2x)],[=(1)/(2)(d)/(dx)(x^(3)-x)=(1)/(2)(3x^(2)-1)],[" 9) i ... See the full answer