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power series

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.
Origin
1890-1895
1890-95
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Examples from the web for power series
  • 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.
British Dictionary definitions for power series

power series

noun
1.
a mathematical series whose terms contain ascending positive integral powers of a variable, such as a0 + a1x + a2x² +…
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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power series in Science
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.
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Encyclopedia Article for 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.
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10
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