Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Radius of convergence? Date: Tue, 10 Feb 2009 02:24:01 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 13 Message-ID: <gmqog1$s4i$1@fred.mathworks.com> References: <gmp919$5sd$1@fred.mathworks.com> <gmpg2v$ba9$1@fred.mathworks.com> <gmpmo1$71h$1@fred.mathworks.com> <gmpvfe$jr3$1@fred.mathworks.com> <gmq63p$ik3$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-02-blr.mathworks.com Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1234232641 28818 172.30.248.37 (10 Feb 2009 02:24:01 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Tue, 10 Feb 2009 02:24:01 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:517206 "Joerg Buchholz" <buchholz@hs-bremen.de> wrote in message <gmq63p$ik3$1@fred.mathworks.com>... > ...... > Roger, > thank you very much for the precise redefinition of my question. Seems like we agree that Matlab cannot 'express that coefficient as a symbolic function of n' with on-board means. Do you think that there is a chance to write an m-file that could do that; or do you believe one could mathematically prove that this is not possible at all? > Joerg Writing such a clever m-file would be a profoundly difficult thing to do, Joerg. To take a comparatively elementary example, consider the expansion of tan(x) about x = 0. According to one of my texts, the x^(2*n-1) term has a coefficient of 2^(2*n)*(2^(2*n)-1)/(2*n)!*Bn where Bn is the n-th Bernoulli number. Unfortunately there is no known single expression for Bn in terms of n as far as I know. It apparently has to be generated using an iterative procedure involving Eulerian numbers starting with n = 1. Taking limits would appear to require information about Bn that would be difficult to put in a form that a general 'limit' function would know how to handle. If one can't hand 'limit' a specific symbolic expression in n, what kind of input, encompassing the properties of Bn as n approaches infinity, could one provide? As is known, the "radius" of convergence here is abs(x) < pi/2, but how would one deduce this from the behavior of Bn? Roger Stafford