# power series

## power series

noun Mathematics.
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.

Origin:
1890–95

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Collins
World English Dictionary
 power series —n a mathematical series whose terms contain ascending positive integral powers of a variable, such as a0 + a1x + a2x² +…

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Science Dictionary
 power series   A sum of successively higher integral powers of a variable or combination of variables, each multiplied by a constant coefficient.
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Encyclopedia Britannica
Encyclopedia

power series

in mathematics, an infinite series that can be thought of as a polynomial with an infinite number of terms, such as 1+x+x2+x3+. Usually, a given power series will converge (that is, approach a finite sum) for all values of x within a certain interval around zero-in particular, whenever the absolute value of x is less than some positive number r, known as the radius of convergence. Outside of this interval the series diverges (is infinite), while the series may converge or diverge when x=r. The radius of convergence can often be determined by a version of the ratio test for power series: given a general power series a0+a1x+a2x2+,in which the coefficients are known, the radius of convergence is equal to the limit of the ratio of successive coefficients. Symbolically, the series will converge for all values of x such that

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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Example sentences
Power series expansion of the solenoid magnetic field.
Use infinite power series to solve higher-order differential equations about ordinary points.
The coefficients in the power series are functions of all the correlation functions of any order for the composite.
Includes utilities for obtaining efficiently the coefficients of polynomials, trigonometric sums and power series.
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