(3) Here we derive the Poisson integral formula for Poisson's equation inside the unit disk. Consider Au = Upr + =Ur + -2190 =0, OrER, OSOS2n, u(R, 0) = f(0), u bounded as r = 0, u, up 2x-periodic in e (a) Use the separation of variables procedure (i.e., write u(r, 0) = g(r)h(0) and substitute into the PDE etc.) to show that u(r, #) can be written as the series u(r, 0) = Ao + (An cos(no) + Bn sin(no))r (b) Determine An, An, and B,, in terms of f(0). (c) Replace the variable of integration in Part (3b) by w. Then use Parts (3a) and (3b) to show that u ( r , 0 ) = 26 5 ( w ) 1 + 2 ) ( 2 ) " cos ( n(w - 0) ) du . (d) Let Lei(w -# ). R so that ( )" cos (n(w - 0)) = Rez" Note that |z|