these 2 questions are related. i included legendres solution

Community Answer

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