Power Series from a Computational Point of View |
Contents
TAYLOR POLYNOMIALS | 1 |
SEQUENCES AND SERIES | 30 |
POWER SERIES AND COMPLEX DIFFERENTIABILITY | 68 |
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analytic continuation analytic functions analytic on G Cauchy Cauchy's Inequalities Cauchy's Integral Formula Cauchy's Integral Theorem Chapter closed path coefficients complex differentiable complex numbers computation connected open set continuation of f converges absolutely cos(z critical point defined DEFINITION differential equation disk with center end point error evaluation example exist f be analytic f is complex fixed follows function f G₁ gives homotopy implies indap initial point interval Iz-a Iz-al Lemma Let f lim sup logarithm lower bound mean value theorem Monodromy Theorem neighborhood open set G path in G Picard's theorem plane point in G polynomial of degree power series Problem Proof of Theorem prove ps(t r₁ radii radius of convergence real numbers sequence series converges shows simply connected sin(x sin(z star shaped tangent Taylor polynomial Taylor's formula THEOREM 2.4 tion unique continuation z-al