Taylor series expansion around the point \(z_0\) of functions analytic in a ball centered at \(z_0\) . Integral along a curve of a power series multiplied by a continuous function. The sum of a power series is an analytic function within the circle of convergence. Derivative of a power series. Uniqueness of the Taylor series expansion. Notable examples of Taylor series expansions. Definition of annulus. Laurent series expansion around the point \(z_0\) of functions analytic in an annulus centered at \(z_0\) . Integral along a curve of a generalized power series multiplied by a continuous function. The sum of a generalized power series is an analytic function within the convergence annulus. Derivative of a generalized power series. Uniqueness of the Laurent series expansion. Notable examples of Laurent series expansions. Multiplication and division of power series.