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  1. en.wikipedia.org › wiki › Power_seriesPower series - Wikipedia

    Power series. In mathematics, a power series (in one variable) is an infinite series of the form. where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.

  2. A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions.

  3. Nov 16, 2022 · A power series about a, or just power series, is any series that can be written in the form, ∞ ∑ n=0cn(x −a)n ∑ n = 0 ∞ c n ( x − a) n. where a a and cn c n are numbers. The cn c n ’s are often called the coefficients of the series. The first thing to notice about a power series is that it is a function of x x.

  4. Learn what a power series is, how to find its coefficients and radius of convergence, and how to use it to approximate functions. Explore common power series such as geometric series and Maclaurin series with examples and exercises.

  5. Dec 21, 2020 · Example 8.6.4 and the work following Example 8.6.3 established relationships between a power series function and "regular'' functions that we have dealt with in the past. In general, given a power series function, it is difficult (if not impossible) to express the function in terms of elementary functions.

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  7. Learn what power series are, how they depend on x-values, and how they can be used to calculate functions. Watch a video and read the comments from other learners and experts.

    • 7 min
    • Sal Khan
  8. Learn how to represent functions as power series, which are infinite sums of powers of x. Explore the properties, convergence, and applications of power series in calculus.

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