### What does **power series** mean?

# Definitions for power series

pow·er se·ries

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **power series**.

### Princeton's WordNet

power seriesnoun

the sum of terms containing successively higher integral powers of a variable

### 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 nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series. In such cases, the power series takes the simpler form Beyond their role in mathematical analysis, power series also occur in combinatorics as generating functions (a kind of formal power series) and in electronic engineering (under the name of the Z-transform). The familiar decimal notation for real numbers can also be viewed as an example of a power series, with integer coefficients, but with the argument x fixed at 1⁄10. In number theory, the concept of p-adic numbers is also closely related to that of a power series.

### ChatGPT

power series

A power series is a series of the form Σaₙ(x-c)ⁿ, where aₙ are the coefficients, x is the variable, c is the center of the series and n is a non-negative integer that runs from 0 to infinity. This series can be understood as a generalization of a polynomial function where instead of having finite terms, we have infinitely many terms. The behavior and convergence of a power series can vary based on the values of aₙ and x.

### Freebase

Power series

In mathematics, a power series is an infinite series of the form where an represents the coefficient of the nth term, c is a constant, and x varies around c. This series usually arises as the Taylor series of some known function. In many situations c is equal to zero, for instance when considering a Maclaurin series. In such cases, the power series takes the simpler form These power series arise primarily in analysis, but also occur in combinatorics and in electrical engineering. The familiar decimal notation for real numbers can also be viewed as an example of a power series, with integer coefficients, but with the argument x fixed at 1⁄10. In number theory, the concept of p-adic numbers is also closely related to that of a power series.

### Matched Categories

### Numerology

Chaldean Numerology

The numerical value of power series in Chaldean Numerology is:

**2**Pythagorean Numerology

The numerical value of power series in Pythagorean Numerology is:

**8**

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"power series." *Definitions.net.* STANDS4 LLC, 2023. Web. 26 Sep. 2023. <https://www.definitions.net/definition/power+series>.

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