Search results
Results from the WOW.Com Content Network
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.
In mathematics, a power series (in one variable) is an infinite series of the form = = + + + … where a n represents the coefficient of the nth term and c is a constant called the center of the series.
A power series about a, or just power series, is any series that can be written in the form, \[\sum\limits_{n = 0}^\infty {{c_n}{{\left( {x - a} \right)}^n}} \] where \(a\) and \({c_n}\) are numbers. The \({c_n}\)’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 \(x\).
Power Series – Definition, General Form, and Examples. The power series is one of the most useful types of series in mathematical analysis. We can use power series to define different transcendental functions including the exponential and trigonometric functions.
To use the Geometric Series formula, the function must be able to be put into a specific form, which is often impossible. However, use of this formula does quickly illustrate how functions can be represented as a power series. We also discuss differentiation and integration of power series.
Power series is a type of infinite mathematical series that involves terms with a variable raised to increasing powers to infinite level. Think of it as an infinite polynomial series , which can be expressed as: \sum_ {n=0}^ {\infty} c_n x^n = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \ldots ∑n=0∞ cnxn =c0 +c1x+c2x2 +c3x3 +…
Use a power series to represent a function. A power series is a series with terms involving a variable. More specifically, if the variable is x x, then all the terms of the series involve powers of x 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. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power.
A power series is a special type of infinite series representing a mathematical function in the form of an infinite series that either converges or diverges. Whenever there is a discussion of power series, the central fact we are concerned with is the convergence of a power series.
Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depend on the chosen x-value, which makes power series a function.