Unit: Sequences and SeriesModule: Power Series Representations of Functions Differentiation and Integration of Power Serieswww.thinkwell.com [email protected]Copyright 2001, Thinkwell Corp. All Rights Reserved. 1631 –rev 06/15/2001• You can do calculus on a power series inside its interval of convergence. • The derivative of the power series ∞=−∑0()nnnaxcis ∞−=−∑11nnnna x c. • The integral of the power series ∞=−∑0nnnis +∞=−++∑101nnnCn. Inside its interval of convergence a power series defines a function that you can differentiate and integrate. Since constant terms disappear during differentiation, you can start the index of the derivative at n=1. There are many ways to integrate a power series.
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.