A model problem for infinite series
- To: mathgroup at smc.vnet.net
- Subject: [mg113204] A model problem for infinite series
- From: Sam Takoy <sam.takoy at yahoo.com>
- Date: Mon, 18 Oct 2010 05:48:53 -0400 (EDT)
Hi, As a follow up to my previous post and to give a little bit more information, I would like to briefly describe a mathematically nonsensical problem which has some of the elements that I need. To solve Laplace's equation for u(r, alpha) on the unit circle subject to Dirichlet boundary conditions U(alpha), one needs to decompose U as a Fourier series, multiply each term by r^|n| and add them back up. The model problem is this. Starting with a boundary condition U0, solve for u and let U1(alpha) = du/dr(evaluated at r=1)*f[alpha], where f[alpha] is relatively simple and infinitely periodic. Repeat for U1 as the boundary condition, and so forth. My hope is that for a given U0, I could obtain the general form of a Fourier coefficient for, say, U5. I assume that at some point, I will have Fourier series with well defined coefficients, but that are not summable analytically and I would like to know if Mathematica could keep it as an infinite series with a general coefficient. Many thanks in advance, Sam