In mathematics, a power series (in one variable) is an infinite series of the form where represents the coefficient of the n th term and c is a constant called the center of the series.

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 …

Nov 11, 2025 · In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series.

Jul 23, 2025 · 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 …

Power series are used to approximate functions that are difficult to calculate exactly, such as tan -1 (x) and sin (x), using an infinite series of polynomials.

A power series will converge provided it does not stray too far from this center. Common problems on power series involve finding the radius of convergence and the Interval of convergence of a …

Dec 3, 2025 · A power series in a variable is an infinite sum of the form where are integers, real numbers, complex numbers, or any other quantities of a given type.

Illustrated definition of Power Series: An infinite series with increasing powers (exponents) of a variable. Like this: a0 + a1x...

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 …

Power series are one of the most useful type of series in analysis. For example, we can use them to define transcendental functions such as the exponential and trigonometric functions (and …