Time-consuming series coefficients

*To*: mathgroup at smc.vnet.net*Subject*: [mg40230] Time-consuming series coefficients*From*: "marchibald" <marchibald at maths.wits.ac.za>*Date*: Thu, 27 Mar 2003 06:49:13 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I have the following function from which I would like to extract the coefficient of z^{50}, and then expand the result as a series in u: f[z_,u_] := Product[1 + u (Exp(zpq^{i - 1}) - 1), {i,50}] where p=q=1/2. The product from i=1 to 10 can be done in a reasonable amount of time, but anything larger takes far too long. Does anyone have an idea of how to expand f[z,u] as a series quickly, or even to extract the coefficient of z^{50} some other way? Thanks, M. Archibald University of the Witwatersrand

**Follow-Ups**:**Re: Time-consuming series coefficients***From:*Daniel Lichtblau <danl@wolfram.com>