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MATH201 Lecture Notes - Lecture 18: Ratio Test, Radius, Alternating Series Test

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19 Sep 2016

School

University of Alberta

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Course

Professor

Mohammad Ali Niksirat

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Document Summary

Given a differential equation, either in the form: Then, the power series method provides a chance to obtain a solution: May use either or as the solution. Note: the power series is an infinite sum of the general form: where the point is called the centre of the power series s(x), and are constants. Then, if p(x) and q(x) are analytic functions at , then the solution can be written as: Definition: the function f is called analytic @ if there exists an interval for some such that f(x) can be represented for some constant. Fact 1: the set of convergence of a power series. Always is an interval , where is the radius of convergence, a non-negative number that could even be . Note: endpoints, , may or may not belong to the set of convergence. Fact 2: if the following limit exits, then the following summation, either: (i) (ii)

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