Analytic Functions When to Use Use this skill when working on analytic-functions problems in complex analysis. Decision Tree 1. Is f analytic at z0? - Check Cauchy-Riemann equations: du/dx = dv/dy, du/dy = -dv/dx - Check if f has power series expansion around z0 - Check if f is differentiable in neighborhood of z0 - and 2. Cauchy-Riemann Verification - Write f(z) = u(x,y) + iv(x,y) - Compute partial derivatives - Verify: du/dx = dv/dy AND du/dy = -dv/dx - 3. Power Series - f(z) = sum {n=0}^{inf} a n (z - z0)^n - Radius of convergence: R = 1/limsup |a n|^(1/n) - 4. Analytic Continuation - Exte…