MATH201 Lecture 20: MATH201(LEC20): Differential EQs w/ Polynomial Coefficients & Power Series
24 Sep 2016
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Recap: assuming that f is analytic @ , then: 1. f must be continuous @ and must be continuously differentiable @ . If are analytic @ , then and are analytic @ . Theorem: if is a regular point for the equation. Such that is obtained through the recursive formula. Since and are arbitrary. are from the expansion of function p(x) and q(x) ie. note: analytic = represented by a convergent power series . Most important functions that are analytic, ie. every polynomial. Analytic of every ie. analytic at all. Analytic of every ie. analytic at all ie. ie. Example 1: solve the ivp using the power series method. Step 4: set to the same exponent by sing as a dummy variable. Step 5: since summation starts at the same number already; move onto next step to combine sum . Step 6: isolate the with the higher place. Note 3: the above expression is the recursive formula.
