P(n,m) = 1/(2^n n!) (1 - x^2)^(m/2) d((x^2 - 1)^n,x,n + m) "Legendre functions" P(0,0) P(1,0) P(1,1) P(1,-1) P(2,0) P(2,1) P(2,2) P(2,-1) P(2,-2) "Verify (1=ok)" P(0,0) == 1 P(1,0) == x P(1,1) == sqrt(1 - x^2) P(1,-1) == -1/2 sqrt(1 - x^2) P(2,0) == 1/2 (3 x^2 - 1) P(2,1) == 3 x sqrt(1 - x^2) P(2,-1) == -1/2 x sqrt(1 - x^2) P(2,2) == 3 (1 - x^2) P(2,-2) == 1/8 (1 - x^2)

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