POWER SERIES Meaning and
Definition
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A power series refers to an infinite series that consists of terms in which a variable, usually denoted as "x," is raised to a non-negative integer power. The general form of a power series is given by Σ( aₙ * xⁿ), where Σ represents the summation notation and aₙ are constant coefficients.
In the context of mathematics, power series are extensively used in the study of functions and their properties. They offer a way to express functions as an infinite sum of polynomial terms of increasing degree. Power series are particularly beneficial for approximation purposes, as they provide a means to estimate the value of a function within a certain range by evaluating a finite number of terms. This makes them valuable in calculus, analysis, and other branches of mathematics.
Convergence is a fundamental concept associated with power series. A power series is said to converge within a specific range of values for 'x' if the infinite sum of its terms converges to a finite value. Conversely, if the sum does not converge, the power series diverges. The radius of convergence, denoted by 'R,' represents the range of values for 'x' within which the power series converges.
Power series have wide-ranging applications in diverse fields such as physics, engineering, and computer science. They provide solutions to differential equations, enable numerical computations, and aid in developing mathematical models. With their ability to represent functions as an infinite sum, power series form a prominent tool in mathematical analysis and computation.
Common Misspellings for POWER SERIES
- oower series
- lower series
- -ower series
- 0ower series
- piwer series
- pkwer series
- plwer series
- ppwer series
- p0wer series
- p9wer series
- poqer series
- poaer series
- poser series
- poeer series
- po3er series
- po2er series
- powwr series
- powsr series
Etymology of POWER SERIES
The word "power series" originated from the combination of two terms: "power" and "series".
The term "power" in mathematics refers to the exponent of a number. It is the value to which a base is raised.
The term "series" in mathematics represents the sum of the terms of a sequence. It refers to listing the terms one after another, often in an infinite sequence.
Therefore, a "power series" is a mathematical series or sequence in which each term is a power of a variable, generally written as a sum of the form:
a₀ + a₁x + a₂x² + a₃x³ + ...
Where the coefficients a₀, a₁, a₂, a₃, etc., are constants and x is a variable. Power series are often used to represent functions as infinite polynomials, allowing for the approximation and manipulation of complicated functions.
Similar spelling words for POWER SERIES
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