Radius of Convergence

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radius of convergence

[′rād·ē·əs əv kən′vər·jəns]
(mathematics)
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.

References in periodicals archive ?
The nonlinear operator IV Qj) can be developed in entire series with a convergence radius equal to infinity

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