circle of convergence

American  

noun

1. Mathematics. a circle associated with a given power series such that the series converges for all values of the variable inside the circle and diverges for all values outside it.

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Example Sentences

In other words, the original series may legitimately be differentiated at any interior point z0 of its circle of convergence.

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

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

The circle of convergence of any of the series has at least one such singular point upon its circumference.

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

Within a common circle of convergence two power series Σ anzn, Σ bnzn can be multiplied together according to the ordinary rule, this being a consequence of a theorem for absolutely convergent series.

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