In mathematics, a power series (in one variable) 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 (for this reason one sometimes speaks of the series as being centered at c). This series usually arises as the Taylor series of some known function; the Taylor series article contains many examples.
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 (under the name of generating functions) and in electrical 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 ⅟10. In number theory, the concept of p-adic numbers is also closely related to that of a power series.
Read more about Power Series: Examples, Radius of Convergence, Analytic Functions, Formal Power Series, Power Series in Several Variables, Order of A Power Series
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