mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either...

Absolute convergence at every point of the boundary: ∑ n = 1 ∞ z n n 2 {\textstyle \sum _{n=1}^{\infty }{\frac {z^{n}}{n^{2}}}} has radius of convergence 1 {\displaystyle...

plane. Bend radius Filling radius in Riemannian geometry Mean radius Radius of convergence Radius of convexity Radius of curvature Radius of gyration Semidiameter...

mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series. It was published in 1821 by Cauchy, but remained...

_{k=0}^{\infty }(-1)^{k}(z-1)^{k}.} By the Cauchy–Hadamard theorem, its radius of convergence is 1. That is, f {\displaystyle f} is defined and analytic on the...

these have poles at c {\displaystyle c} , and inner radius of convergence 0, so they both converge on an overlapping annulus. Thus when defining formal...

not converge if x is far from b. That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The...

from it Radius of convergence (in calculus), the radius of the region where a complex power series converges Radius of curvature, a measure of how gently...

Domain of convergence of power series Riemann series theorem – Unconditionally convergent series converge absolutely Unconditional convergence – Order-independent...

a_{k}} with radius of convergence 1. {\displaystyle 1.} Suppose that the series ∑ k = 0 ∞ a k {\displaystyle \sum _{k=0}^{\infty }a_{k}} converges. Then G...