The following errors worthy of note were made in your Homework 9 solutions. (See the complete solutions posted to the usual UDrive location.)

- Forgot to state explicitly what function is holomorphic where; forgot to name the theorem used (“Cauchy’s Integral Formula”).
- Forgot to state explicitly what function is holomorphic where; forgot to name the theorems used (“Cauchy’s Integral Formula for Derivatives” or “Cauchy’s Integral Formula”).
- Failed to specify a contour over which the integration takes place [need to say that you use any contour from 0 to
*z*in the disk*D*_{1}(0)]; forgot to note that the singularities of Arctan, at ±*i*, are not in the open disk*D*_{1}(0). - In (a), fallaciously claimed that
*f*is differentiable at 0 because it is continuous at 0 (you need to verify directly that*f*is differentiable at 0); fallaciously claimed that*f*is holomorphic at 0 because it is differentiable there (you have to note also that*f*is differentiable at all*z*≠ 0). - On some solutions, found a series expansion on a disk |
*z*−*i*| < √2 instead of on the “annulus” |*z*−*i*| > √2. - (no notable errors)
- (l) Forgot that sinh(0) = 0, too [which means the pole
*z*= 0 has order only 5 − 1 = 4, and*not*5]. - (b) not common, but an error worthy of mention: mistakenly wrote formula as

lim_{ z →z0}(*z*−*z*_{0})^{3}(d^{2}/d*z*^{2})[*f*(*z*)] instead of the correct version lim_{ z →z0}(d^{2}/d*z*^{2})[(*z*−*z*_{0})^{3 }*f*(*z*)] - no common errors other than miscalculation
- no common errors other than miscalculation