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
Famous quotes containing the words power and/or series:
“One cannot demand of a scholar that he show himself a scholar everywhere in society, but the whole tenor of his behavior must none the less betray the thinker, he must always be instructive, his way of judging a thing must even in the smallest matters be such that people can see what it will amount to when, quietly and self-collected, he puts this power to scholarly use.”
—G.C. (Georg Christoph)
“Every man sees in his relatives, and especially in his cousins, a series of grotesque caricatures of himself.”
—H.L. (Henry Lewis)