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 December 28th, 2014, 06:50 AM #1 Senior Member   Joined: Sep 2010 From: Oslo, Norway Posts: 162 Thanks: 2 Is finding laurent series expansion of f at z_0 using geometric series convenient? Hello there, I was taught in my complex analysis course that I can find the laurent series expansion for $f:\Omega \to \mathbb{C}$ by using the formula for geometric series: $$f(z) = \frac{1}{1-g(z)} = \sum_{n=0}^\infty g(z)^n$$ This is useful for series expanded at $z=0$. However, I am interested in finding convenient methods for making laurent expansions at at other points $z_0$. I would like to make series of the form: $$f(z) = \sum_{n=-\infty}^\infty a_n(z-z_0)^n,$$ where $z_0$ may be different for $0$. Is it convenient to use the geometric series construction to do this? If so, how? And if not, which are the convenient methods to do so? I know that the coefficients are given by $a_n = 1/(2\pi i) \oint_C f(z)/(z-z_o)^{n+1} \mathrm{d}z$, but it is tedious to calculate all the coeffients manually. Thank you for your time. Kind regards, Marius Last edited by king.oslo; December 28th, 2014 at 07:44 AM. Tags convenient, expansion, finding, geometric, laurent, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Complex Analysis 7 May 5th, 2014 11:09 PM The Chaz Real Analysis 11 February 7th, 2011 04:52 AM eljose Calculus 1 July 17th, 2010 09:16 AM eskimo343 Complex Analysis 1 December 3rd, 2009 10:33 AM pascal4542 Complex Analysis 2 December 3rd, 2009 10:19 AM

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