radius of convergence

American  

noun

Mathematics.

1. a positive number so related to a given power series that the power series converges for every number whose absolute value is less than this particular number.

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Example Sentences

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radius of convergence

The ratio test may often be used to determine the radius of convergence.

From Textbooks ● Mar. 30, 2016

Note that although Term-by-Term Differentiation and Integration for Power Series guarantees the same radius of convergence when a power series is differentiated or integrated term-by-term, it says nothing about what happens at the endpoints.

From Textbooks ● Mar. 30, 2016

The interval of convergence is the single value x = 0 and the radius of convergence is R = 0.

From Textbooks ● Mar. 30, 2016

In this case, we say that the radius of convergence is R = 0.

From Textbooks ● Mar. 30, 2016

If for every position of z0 this is the greatest radius of convergence of the derived series, then the original series represents a function existing only within its circle of convergence.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" by Various