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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



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