Re: Searching list for closest match to p
- To: mathgroup at smc.vnet.net
- Subject: [mg79418] Re: [mg79274] Searching list for closest match to p
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Thu, 26 Jul 2007 05:34:21 -0400 (EDT)
- References: <200707230741.DAA22149@smc.vnet.net>
chuck009 wrote: > I'm working on an interesting theorem in Complex Analysis called Jentzsch's Theorem in which the zeros of the partial sums of a Taylor series for an analytic function in the unit disk, all converge to values on the unit disk. So I choose a point on the unit disk, p=Cos[pi/3]+iSin[pi/3], calculate the normal series for f[x]=Log[1+x] for n ranging from 1 to 100, calculate the zeros, then for each polynomial, search the zeros for the one closest to the point. Here's my code. I feel the Table part is messy with the First[First[Position... construct in it. Can anyone recommend a more concise way of searching the zero lists and finding the one closest to p3? > > Thanks, > [...] Corrected wording is that the collection of zeros of partial sums converge to all values on the unit disk (note juxtaposition vs. "all converge to"). I'd like someone to contribute an illustration of this result to the demonstrations.wolfram.com web site.* A possibility would be to have buttons to switch between a few possible functions with radius of convergence equal to one, a locator for the point on the circle, and have a slider that takes ever increasing partial sums of power series. It would then show those roots of the sums that get closer to the locator than roots of prior sums, perhaps making the color get of the points change as a function of proximity to the locator on the circle. Daniel Lichtblau Wolfram Research * I'm prepared to be insufferable until I get one I like.
- References:
- Searching list for closest match to p
- From: chuck009 <dmilioto@comcast.com>
- Searching list for closest match to p