From the course: Complete Guide to Differential Equations Foundations for Data Science
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Power series
From the course: Complete Guide to Differential Equations Foundations for Data Science
Power series
- [Instructor] Let's start off by exploring how to use power series to solve differential equations. Before I dive into how to use these to solve differential equations, let's take some time to understand exactly what power series are. Power series are a type of series used to sum up an infinite amount of terms. Note that you could technically have a power series with a finite amount of terms it is summing, but I will focus on the infinite term case in this course. The terms usually involve some sort of power on the variable, hence the name power series. These series are often thought of as infinite polynomials due to the functions they represent or create with their ever-increasing power terms. Power series are in the form of f of x equals the sum of n equals zero to infinity of a of n multiplied by x minus x naught to the n. Here you have the real numbers, a n, and x naught with a n being a constant value. Then you have your variable x and your power n, which is also a real number…
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