2

In a Taylor series, the convergence/divergence behavior at the boundary case $|x-x_0|=R$ is not immediately determinable.

If I understand correctly, such distribution of convergence and divergence over the spherical shell can be thought as $S^n\mapsto \hat{\mathbb{C}}$, and this distribution is a function of the original function for which the Taylor series was defined. Is there an extended study done on this subject?

Willie Wong
  • 73,139
finnlim
  • 2,733
  • 1
    I don't fully understand your question, but this MO post seems to be relevant: http://mathoverflow.net/questions/49395/behaviour-of-power-series-on-their-circle-of-convergence. – Srivatsan Apr 04 '12 at 04:42
  • Possible duplicate to http://math.stackexchange.com/questions/82871/examples-of-taylor-series-with-interesting-convergence-along-the-boundary-of-con which is also linked to by the MO post Srivatsan mentioned. Given the dearth of literature there probably isn't an "extended" study on the subject. – Willie Wong Apr 04 '12 at 08:21

0 Answers0