Derivative[1][w][z]^6 (-1 + Derivative[1][w][z]^2) (27 m^2 n + 4 (m - n)^3 Derivative[1][w][z]^2)^2 (1 + (-1 + m) (-1 + n)^2 Derivative[1][w][z]^2) + Derivative[1][w][z]^4 (-243 m^4 n^2 - 9 m^2 n (-3 m (-12 + n) n^2 - 10 n^3 + 3 m^2 n (4 + n (-16 + 3 n)) + m^3 (16 + 6 n (-5 + 3 n))) Derivative[1][w][z]^2 - 2 (m - n)^2 (2 m (-10 + n) n^3 + 4 n^4 - 3 m^2 (-9 + n) n^2 (-1 + 2 n) + 4 m^4 (-1 + n) (-2 + 3 n) + m^3 n (8 + 3 (5 - 11 n) n)) Derivative[1][w][z]^4 + 8 (-1 + m) (m - n)^5 (-1 + n) n Derivative[1][w][z]^6) Derivative[2][w][z]^2 + n Derivative[1][w][z]^2 (-27 m^4 n - m^2 (m - n)^2 (-10 n + m (-8 + 9 n)) Derivative[1][w][z]^2 + (-1 + m) (m - n)^4 n Derivative[1][w][z]^4) Derivative[2][w][z]^4 - m^4 n^2 Derivative[2][w][z]^6 == 0 /; w[z] == EllipticPi[n, z, m]

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2001-10-29