5. This problem outlines a "bar room" proof of Cauchy's Integral Formula Assume Ω is a simply con...
5. This problem outlines a "bar room" proof of Cauchy's Integral Formula Assume Ω is a simply connected domain. Let f(z) be holomorphic on and suppose zo E S2. We know and inside Ω f(3) cr 220 f(e) dz where C is a circle centered at zo with radius r. (a) Express z-zo + reit where r is given by C and t [0,2 ] and rewrite the above integral in polar form. (b) From (a) let r-0 in the integrand. Then integrate and find f(2) an 20 (c) What lacked rigor with what you did in part (5B)?
5. This problem outlines a "bar room" proof of Cauchy's Integral Formula Assume Ω is a simply connected domain. Let f(z) be holomorphic on and suppose zo E S2. We know and inside Ω f(3) cr 220 f(e) dz where C is a circle centered at zo with radius r. (a) Express z-zo + reit where r is given by C and t [0,2 ] and rewrite the above integral in polar form. (b) From (a) let r-0 in the integrand. Then integrate and find f(2) an 20 (c) What lacked rigor with what you did in part (5B)?