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racland
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Anyone knows anything about the Radius on convergence in the complex plane (Complex Analysis)
DeadWolfe said:Yes. Somebody knows something about the radius of convergence in the complex plane.
Hope I was helpful
The radius of convergence refers to the maximum distance from the center of a power series in the complex plane within which the series will converge.
The radius of convergence can be determined by using the ratio test, which involves taking the limit of the absolute value of the ratio of successive terms in the series.
The radius of convergence is important because it tells us the distance from the center of the series within which the series will converge. If a point is outside the radius of convergence, the series will diverge at that point.
Yes, the radius of convergence can be infinite, meaning the series will converge for all points in the complex plane. This occurs when the series has a limit of zero at infinity.
The radius of convergence affects the behavior of a power series by determining where the series is convergent and where it is not. It also helps us to determine the interval of convergence, which is the range of values for which the series will converge.