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A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).
More generally, formal power series can include series with any finite (or countable) number of variables, and with coefficients in an arbitrary ring. Rings of formal power series are complete local rings, which supports calculus-like methods in the purely algebraic framework of algebraic geometry and commutative algebra. They are analogous to ...
Perturbation theory develops an expression for the desired solution in terms of a formal power series known as a perturbation series in some "small" parameter, that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the ...
In mathematics, a power series (in one variable) is an infinite series of the form = = + + + … where represents the coefficient of the nth term and c is a constant called the center of the series. Power series are useful in mathematical analysis , where they arise as Taylor series of infinitely differentiable functions .
In mathematics, the Bell series is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell . Given an arithmetic function f {\displaystyle f} and a prime p {\displaystyle p} , define the formal power series f p ( x ) {\displaystyle f_{p}(x)} , called the Bell series ...
In mathematics and computer science, a rational series is a generalisation of the concept of formal power series over a ring to the case when the basic algebraic structure is no longer a ring but a semiring, and the indeterminates adjoined are not assumed to commute.
Like the book, the series tells the story of Elizabeth Zott (Brie Larson), a young woman who’s dead-set on working as a chemist despite the odds stacked against her in 1950s America.
In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by S. Bochner ( 1946 ). The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations.