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Rings of Formal Power Series

Canadian Mathematical Bulletin, 1971
In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
N. Sankaran
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Formal Power Series

, 2016
We begin here the subject of formal power series, objects of the form \(\displaystyle \sum _{n=0}^{\infty }a_nX^n\) (\(a_n\in \mathbb R\) or \(\mathbb C)\) which can be thought as a generalization of polynomials. We focus here on their algebraic properties and basic applications to combinatorics.
Mariconda C., Tonolo A.
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Controllability of (max,+) Formal Power Series

IFAC Proceedings Volumes, 2009
Controllability of (max,+) automata and formal power series is studied within a behavioral framework. An extension of classical tensor product of their linear representations as a parallel composition of controller with the plant (max,+) automaton is used.
Komenda, Jan, Lahaye, Sébastien, Boimond, Jean-Louis   +2 more
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On n-associative formal power series

Aequationes Mathematicae, 2015
In general, a formal power series \(F(x_1,\dots,x_n)\in\mathbb{C}[[x_1,\dots,x_n]]\), can be substituted into a formal power series if and only if \(F(0,\dots,0)=0\), which means that \(\mathrm{ord}(F)\geq 1\). For \(n\geq 3\) consider a formal power series \(F(x_1,\dots,x_n)\in\mathbb{C}[[x_1,\dots,x_n]]\) with \(\mathrm{ord}(F)\geq 1\).
Harald Fripertinger
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Inverting Polynomials and Formal Power Series

SIAM Journal on Computing, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Formal Power Series

, 1993
This chapter discusses a variety of algorithms for manipulating formal power series. Formal power series are infinite power series where we are not concerned with issues of convergence. Thus, both f(t) and g(t) $$ \begin{array}{*{20}{c}} {f\left( t \right) = 1 + t + \frac{{{t^2}}}{{2!}} + \frac{{{t^3}}}{{3!}} + \frac{{{t^4}}}{{4!}} + \cdots ,} \\ {g\
Koepf, Wolfram, Gruntz, Dominik
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Substitution Groups of Formal Power Series

Canadian Journal of Mathematics, 1954
In this paper we are concerned with the group of formal power series of the form,the coefficients being elements of a commutative ring R and the group operation being substitution. Little seems to be known of the properties of groups of this type, except in special cases, although groups of formal power series in several variables with complex ...
S. A. Jennings
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Associative formal power series in two indeterminates [PDF]

Semigroup Forum, 2013
peer reviewedInvestigating the associativity equation for formal power series in two variables we show that the transcendental associative formal power series are of order one or two and that they can be represented by an invertible formal power series ...
Harald Fripertinger, Ludwig Reich, Fripertinger Harald   +2 more
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On universal formal power series

Journal of Mathematical Analysis and Applications, 2008
The point source of this work is Seleznev's theorem which asserts the existence of a power series which satisfies universal approximation properties in C∗. The paper deals with a strengthened version of this result.
Augustin Mouze
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Formal power series

Annals of Mathematics and Artificial Intelligence, 1996
Power series are familiar to people working in theoretical computer science, since they are accustomed to considering such series with arbitrary exponents and coefficients, and they know what the series notation means: the distributivity of the multiplication over the infinite sum. Here, we will be interested in the ring structure the set of all series
Lee A. Rubel, James E. Colliander
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