# How to do power series?

Date created: Sat, Jul 3, 2021 8:43 PM

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Date created: Sun, Jul 4, 2021 3:59 AM

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.

Date created: Sun, Jul 4, 2021 6:50 AM

Now all we need to do to get a power series representation is to replace the \(x\) in \(\eqref{eq:eq3}\) with \(\frac{x}{5}\). Doing this gives, \[g\left( x \right) = \frac{1}{5}\,\,\sum\limits_{n = 0}^\infty {{{\left( {\frac{x}{5}} \right)}^n}} \hspace{0.5in}{\mbox{provided }}\left| {\frac{x}{5}} \right| < 1\]

Date created: Sun, Jul 4, 2021 12:37 PM

In short, power series offer a way to calculate the values of functions that transcend addition, subtraction, multiplication, and division -- and they let us do that using only those four operations. That gives us, among other things, a way to program machines to calculate values of functions like sin (x) and sqrt (x).

Date created: Sun, Jul 4, 2021 8:13 PM

Where w is set to w = (z – z 0) (Wilde, 2006).. Power Series Integration. Integration is a relatively simple procedure for representing an integrated function as an equivalent series summation.. Integration is particularly useful for functions that are not easily interchanged into a typical summation. The Integration step allows for the interchangeability from function to summation.

Date created: Mon, Jul 5, 2021 12:10 AM

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.

Date created: Mon, Jul 5, 2021 2:47 AM

Calculating power for series and parallel circuits is really nice compared to calculating current and voltage for series parallel circuits, you just multiply the voltage across a component by the current through the component, and add that product to the product of voltage and current for all other components.

Date created: Mon, Jul 5, 2021 6:23 AM

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Date created: Mon, Jul 5, 2021 10:54 AM

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