MATH 2Z03 Lecture Notes - Lecture 11: Quadratic Equation, Frobenius Method, Creative Commons License

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Analytic: will have a taylor series expansion that expands at the given point; i. e. will not have a denominator that is 0; functions with singular points are not analytic e. g. 3) This is not in standard form. y x. Find series solution centred at the ordinary point, you are guaranteed to find at least 2 solutions about an ordinary point. They"ll converge everywhere between the nearest singular points. You are guaranteed to find it because x < . Every time you differentiate you kill the first term, a constant. y n n. Note: look at the ode in standard form only to find the ordinary/singular points. The point of the power series is to find the coefficients. The sum of each set of things with the same power of x is 0. First, let"s distribute the x: nc x n. 2 n c x n n nc x n.