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

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source Link To power series
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
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
Cite This Source
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.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source
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

Learn more about power series with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
Cite This Source
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.
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature
FAVORITES
RECENT

;