Hello,
Please I use below code to calculate partial derivative of U with respect to r and y. I have couple of questions.
I know the derivative of E(k) =(E(k)-K(k))/k. However, the result shows that the answer is E(k) =(E(k)-K(k))/2*k. I do not know why there is 2 in denominator.
Where K(k) and E(k) are complete elliptical integral kind one and two
Clear[r, y, Y, k, U, Ur, Uy]
k = r^3 + y^3;
U := EllipticE[k];
Ur = D[U, y] // FullSimplify
Uy = D[U, r] // FullSimplify
Result from Mathematica is
(3 y^2 (EllipticE[r^3 + y^3] - EllipticK[r^3 + y^3]))/(2 (r^3 + y^3))
(3 r^2 (EllipticE[r^3 + y^3] - EllipticK[r^3 + y^3]))/(2 (r^3 + y^3))
The answer should be
(3 y^2 (EllipticE[r^3 + y^3] - EllipticK[r^3 + y^3]))/((r^3 + y^3))
(3 r^2 (EllipticE[r^3 + y^3] - EllipticK[r^3 + y^3]))/((r^3 + y^3))
Thanks