Results 271 to 280 of about 966,035 (317)
Some of the next articles are maybe not open access.
On the Summability of Power Series
The Annals of Mathematics, 1932if a = 0. 4 The last restriction is unnecessary in the case of a function integrable in the Lebesgue sense. It arises from the fact that the nth Fourier coefficient is o (n), and examples show that this cannot be improved, even in the case of a function integrable in the Cauchy-Lebesgue sense. "Paley (15).
openaire +4 more sources
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.
openaire +1 more source
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.
openaire +1 more source
Canadian Journal of Mathematics, 1964
In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomialsare constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared.
Cheney, E. W., Sharma, A.
openaire +1 more source
In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomialsare constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared.
Cheney, E. W., Sharma, A.
openaire +1 more source
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
openaire +2 more sources
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
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
Short-term prediction of PV power based on fusions of power series and ramp series
Electric Power Systems Research, 2023Xianjun Qi
exaly
Complex series and power series
1992Abstract We begin this chapter with some introductory remarks to motivate the study of complex power series. As we shall see in Chapter 14, such series turn out to be fundamental in the theory of holomorphic functions. We should like to have complex analogues of these.
openaire +1 more source