radius of convergence of a complex function
For example, the function is analytic inside the disk . Hence its the radius of covergence of its Taylor series about is at least . By direct examination of the Taylor series we can see that its radius of convergence is, in fact, equal to .
Colloquially, this theorem is stated in the sometimes imprecise but memorable form “The radius of convergence of the Taylor series is the distance to the nearest singularity.”
|Title||radius of convergence of a complex function|
|Date of creation||2013-03-22 14:40:33|
|Last modified on||2013-03-22 14:40:33|
|Last modified by||rspuzio (6075)|