Independent variable can have value {radius of convergence} {convergence radius} greater than zero at which power series changes from convergence to divergence. Power series, power-series differential, and power-series integral have same convergence radius.
For complex-number power series, if complex number lies within a complex-plane circle {convergence circle} {circle of convergence} centered on zero, with no singularities, series converges. If complex number lies outside a complex-plane circle, series diverges.
Laurent series has complex number that lies within annulus in complex plane {convergence annulus} {annulus of convergence}.
Independent variable can have values {region of convergence} {convergence region, series} for which series converges.
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Date Modified: 2022.0225