MATH 2Z03 Study Guide - Final Guide: Analytic Function, Frobenius Method
16 Jan 2017
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Frobenius"s theorem actually says to guess: y x r x. I describe what those mean here, but you generally won"t need to. However, most of the time (i. e. when your function is analytic), you"ll be dealing with an r = 0 and 0. You may only add sums with the same starting n. keep in mind that you can change the power of x by changing the starting n: n n. Think of it this way: whatever you subtract from the value of the starting n, you take away from the other n"s in the sum. Another thing is that you can increase the starting n by taking out the first couple of terms: Group everything with the same power of x. This is how you determine the values of your constants. The goal of power series is to make all the x"s inside the summation have the same power.
