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Proceedings of the Physico-Mathematical Society of Japan. 3rd Series, 1932 Some of the next articles are maybe not open access.
On the Summability of Power Series
Proceedings of the London Mathematical Society, 1932The author \(1^\circ\) gives a necessary and sufficient condition for the summability \((C, \gamma)\) of the power series \(f(z) =\sum a_nz^n\), \(a_n =o(n^\gamma)\) \((\gamma > -1)\) on the circle \(| z| = 1\), \(2^\circ\) applies the condition to obtain some (mostly known) theorems on the summability of power series, bounded (or even satisfying a ...
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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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Canadian Journal of Mathematics, 1964
In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomials are constructed in correspondence with a function f ∊ C
Cheney, E. W., Sharma, A.
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In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomials are constructed in correspondence with a function f ∊ C
Cheney, E. W., Sharma, A.
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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
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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
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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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Software: Practice and Experience, 1980
AbstractThe creation, manipulation and evaluation of univariate infinite power series is discussed. Unlike truncated power series, which store the first n terms of an expansion, infinite power series create a procedure for calculating a general term, and are thus a formal representation of the entire expansion.
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AbstractThe creation, manipulation and evaluation of univariate infinite power series is discussed. Unlike truncated power series, which store the first n terms of an expansion, infinite power series create a procedure for calculating a general term, and are thus a formal representation of the entire expansion.
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Series of functions and power series
2015The idea of approximating a function by a sequence of simple functions, or known ones, lies at the core of several mathematical techniques, both theoretical and practical. For instance, to prove that a differential equation has a solution one can construct recursively a sequence of approximating functions and show they converge to the required solution.
Claudio Canuto, Anita Tabacco
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Taylor Series and Power Series
2009In Chap. 5 we showed that the sum of a geometric series is given by $$1+x+x^{2}+x^{3}+\cdots=\frac{1}{1-x}$$ This formula holds true for ...
Klaus Weltner +3 more
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