Suppose you have a complex-valued function of a complex variable (namely, ##z=x+iy, \, \, x,y\in \mathbb{R}##) defined as the assumed convergent infinite product
$$F(z)=\prod_{k=1}^{\infty}f_{k}(z)$$
Further suppose ##F(x+iy)=u(x,y)+i v(x,y)##, where u and v are real-valued functions.
How to...