- #1

zardiac

- 16

- 0

## Homework Statement

Assume that u is harmonic everywhere in R^2, and let

[tex]v(x,y)=\int_0^y u_x'(x,t)dt - \int_0^x u_y'(s,0)ds[/tex]

show that f=u+iv is entire analytic.

## Homework Equations

Maybe Cauchy Riemann: [tex]u_x'=v_y'[/tex] and [tex]u_y'=-v_x'[/tex]

## The Attempt at a Solution

I have only tried to see what happens if I use the Cauchy Riemann equations, but I get stuck right away. I am not sure how to use the fact that u is harmonic either.

Any hints would be very appreciated.