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On n-associative formal power series
Aequationes mathematicae, 2015In 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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Annals of Mathematics and Artificial Intelligence, 1996
We consider the formal power series f (z) = a 0 + a{in1z + a 2 z 2+…, which we usually normalize by a 0 = 0.
Lee A. Rubel, James E. Colliander
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We consider the formal power series f (z) = a 0 + a{in1z + a 2 z 2+…, which we usually normalize by a 0 = 0.
Lee A. Rubel, James E. Colliander
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Journal of Automated Reasoning, 2010
This paper presents a formalization of the topological ring of formal power series in \texttt{Isabelle/HOL}. The following constructions are formalized: division, the formal derivative, various basic manipulations on formal power series (shifting, differentiating, general convolutions and powers), as well as radicals, composition and reverses.
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This paper presents a formalization of the topological ring of formal power series in \texttt{Isabelle/HOL}. The following constructions are formalized: division, the formal derivative, various basic manipulations on formal power series (shifting, differentiating, general convolutions and powers), as well as radicals, composition and reverses.
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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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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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Semirings of Formal Power Series
Southeast Asian Bulletin of Mathematics, 2000Let \((S,+,\cdot)\) be an additively commutative semiring with absorbing zero 0 and identity \(1\not=0\). An element \(a\in S\) is called semi-invertible if there are \(s,t\in S\) such that \(1+ra=sa\) and \(1+ar=as\). The set \(U\) of all semi-invertible elements of \(S\) is a subsemigroup of \((S,\cdot)\), \(M=S\setminus U\) is the union of all ...
Adhikari, M. R., Sen, M. K.
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2011
This chapter is somewhat different from the other chapters in this book. It contains not many symbolic sums, hardly any recurrence equations, and only few asymptotic estimates. We provide here the algebraic background on which the notion of a generating function rests.
Manuel Kauers, Peter Paule
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This chapter is somewhat different from the other chapters in this book. It contains not many symbolic sums, hardly any recurrence equations, and only few asymptotic estimates. We provide here the algebraic background on which the notion of a generating function rests.
Manuel Kauers, Peter Paule
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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.
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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.
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Controllability of (max,+) Formal Power Series
IFAC Proceedings Volumes, 2009Controllability 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 +2 more
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Formal Power Series and B-Series
2010We study vector fields, their associated dynamical systems and phase flows together with their algorithmic approximations in R N from the formal power series approach.
Kang Feng, Mengzhao Qin
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Schur’s criterion for formal power series
Sbornik: Mathematics, 2019Abstract A criterion for when a formal power series can be represented by a formal Schur continued fraction is stated. The proof proposed is based on a relationship, revealed here, between Hankel two-point determinants of a series and its Schur determinants. Bibliography: 10 titles.
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