Radius of Convergence(redirected from Convergence radius)
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radius of convergence[′rād·ē·əs əv kən′vər·jəns]
The positive real number corresponding to a power series expansion about some number a with the property that if x-a has absolute value less than this number the power series converges at x, and if x-a has absolute value greater than this number the power series diverges at x.
Radius of Convergence
The radius of convergence of a power series is the radius of the circle of convergence. In other words, it is the number r such that the power series
converges when ǀzǀ > r and diverges when ǀzǀ > r.