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 · When we talk about a converging power series, we mean that as you add more terms, the series approaches a finite value. The key concepts here are the radius of …

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.

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

Power series is closely linked to the topic of Taylor series as it can be used to approximate certain functions about the value x = c x = c. Any power series can give an approximation about the …

Nov 14, 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.

power series, in mathematics, an infinite series that can be thought of as a polynomial with an infinite number of terms, such as 1 + x + x2 + x3 +⋯.

Oct 27, 2023 · Power series are mostly used for Taylor series. This allows us to work with functions by taking polynomial approximations with control about the error.