power series

American  

noun

Mathematics.

1. an infinite series in which the terms are coefficients times successive powers of a given variable, or times products of powers of two or more variables.

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power series British  

noun

1. a mathematical series whose terms contain ascending positive integral powers of a variable, such as a 0 + a 1 x + a 2 x ² +…

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power series Scientific  

1. A sum of successively higher integral powers of a variable or combination of variables, each multiplied by a constant coefficient.

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Etymology

Origin of power series

First recorded in 1890–95

Example Sentences

In the following exercises, use partial fractions to find the power series of each function.

From Textbooks • Mar. 30, 2016

First, we state Term-by-Term Differentiation and Integration for Power Series, which provides the main result regarding differentiation and integration of power series.

From Textbooks • Mar. 30, 2016

We show how power series can be used to evaluate integrals involving functions whose antiderivatives cannot be expressed using elementary functions.

From Textbooks • Mar. 30, 2016

In the previous two sections we discussed how to find power series representations for certain types of functions––specifically, functions related to geometric series.

From Textbooks • Mar. 30, 2016

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