- #1
Stephen88
- 61
- 0
_z=conjugate
p_g=partial diff
_p_g=conjugate pde
p_g_x=partial diff with respect to x
Suppose that f : D → C . Let g(z) : D → C be defined by
g(z) = f(_z). Calculate_p_g and p_g where _p_g=(p_g_x+i(p_g_y))/2, p_g=(p_g_x+i(p_g_y))/2;
Conclude that f is holomorphic on D if
and only if p_g = 0 on D.
I've calculated the pde and observed that I get different signs that supposed to for a regular exercise.Also there is a property that states that f is holomorphic if _p_g=0...given the nature of the function g(z) by intuition am assuming that in this case is has to be the other way around.
Any help will be great Thank you.
p_g=partial diff
_p_g=conjugate pde
p_g_x=partial diff with respect to x
Suppose that f : D → C . Let g(z) : D → C be defined by
g(z) = f(_z). Calculate_p_g and p_g where _p_g=(p_g_x+i(p_g_y))/2, p_g=(p_g_x+i(p_g_y))/2;
Conclude that f is holomorphic on D if
and only if p_g = 0 on D.
I've calculated the pde and observed that I get different signs that supposed to for a regular exercise.Also there is a property that states that f is holomorphic if _p_g=0...given the nature of the function g(z) by intuition am assuming that in this case is has to be the other way around.
Any help will be great Thank you.