Category Archives: Mathematical Physics

Complex Analysis Part 2

Liouville’s Theorem If a function $f(z)$ is analytic for all finite values of z, and is bounded then it is a constant.Note:- $e^{z+2\pi i} = e^z$ Taylor’s TheoremIf a function $f(z)$ is analytic at all points inside a circle C, with its centre at point a and radius R then at each point z inside C$f(z)=f(a)+(z-a)f'(a)+\frac{1}{2!}(z-a)^2f”(a)+…….+\frac{1}{n!}(z-a)^nf^n(a)$Taylor’s theorem is applicable when function is analytic at all points inside a circle.  Laurent SeriesIf $f(z)$ is … Continue reading Complex Analysis Part 2 »