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The rank of a formal tree power series
Theoretical Computer Science, 1983 A formal power series on trees is a mapping from a free algebra \(T_{\Sigma}\) into a field K; recall that \(\Sigma\) is a set of symbols of functions \(\Sigma =\Sigma_ 0\cup...\cup \Sigma_ n\cup...\) and that \(T_{\Sigma}\) (the set of trees) is defined inductively by: \(\Sigma_ 0\subset T_{\Sigma};\) if \(f\in \Sigma_ n\) and \(t_ 1,...,t_ n\in T_ ...
Bozapalidis, S., Louscou-Bozapalidou, O.
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Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients
Discrete Dynamics in Nature and Society, 2006 This paper studies reciprocals of formal power series whose coefficients are monotone and bounded by a geometrically decaying sequence. Explicit and applicable, optimal decay rates are provided for the coefficients of the reciprocal series in terms of ...
Kenneth S. Berenhaut +2 more
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Fast Algorithms for Manipulating Formal Power Series [PDF]
Journal of the ACM, 1978 Computer Science ...
Richard P. Brent, H. T. Kung 0001
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Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i MehanikaLet D be a Dedekind domain of characteristic zero, let K be the fraction field of D, and consider the Cauchy problem ay′ = byᵐ, y(0) = c₀, in the ring D[[x]], where a, b, c₀ ∈ D, a, b ≠ 0, and m ∈ ℕ.
Roman Skurikhin
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Recognizable formal power series on trees
Theoretical Computer Science, 1982 Trees are a very basic object in computer science. They intervene in nearly a;ly domain, and they are studied for their own, or used to represent conveniently a given situation. There are at least three directions where investigations on trees themselves are motivated, and this for different reasons.
Berstel, Jean, Reutenauer, C.
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The multidimensional generalization of Bauer's g-algorithm
Karpatsʹkì Matematičnì Publìkacìï, 2013 The algorithm for the expansion of the given formal multiple power series into the corresponding multidimensional g-fraction with independent variables is constructed and the conditions of existence of such algorithm are established.
R. I. Dmytryshyn
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A Lifting Theorem for Formal Power Series [PDF]
Proceedings of the American Mathematical Society, 1974 We define a class of operations on formal power series that includes practically all operations of interest. The class is closed under composition. We prove that an operation in this class vanishes for complex numbers if and only if it vanishes for functions analytic at the origin. A variety of applications of this “lifting theorem” are discussed.
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Puiseux series solutions of ODEs
Electronic Journal of Differential Equations, 2015 In this article, we will determine Puiseux series solutions of ordinary polynomial differential equations. We also study the binary complexity of computing such solutions.
Ali Ayad +3 more
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On convergence sets of formal power series
Complex Analysis and its Synergies, 2015 17 ...
Ma, Daowei, Neelon, Tejinder S.
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