Here Fk(zk) are analytic functions of the complex variables zk x + UkY
(k 1,2,3) and Ai, A2, A3 are the complex numbers equal to
/2(11)
A2 3( 2) (A. 44)
2(12)
A = 13(-3)
14(p3)
Now we introduce new functions of the complex variable Zk,
,(zk) F(zk) k 1,2
3) (FZ3) (A.45)
Taking the derivative of F and b with respect to x and y respectively results as
JR 2R e[ i1(z 1) + (22( 2) + ( 3)] + '
6x 6x
6F 6Fo
W = 2 Re[pi1i(zi) +p/22(z2) +/3A303(z3)1 + (A.. )
6F
W 2Re[A~l1(z1) + A202(z2) + 03(3)] +',
6x