Further Applications of the Integral and Taylor Polynomials

Calculus ◽  
2015 ◽  
pp. 443-477
Author(s):  
Jon Rogawski ◽  
Colin Adams
Keyword(s):  
Taylor Polynomials

Taylor Polynomials and Approximation

Calculus ◽  
1984 ◽  
pp. 667-688
Author(s):  
STANLEY I. GROSSMAN
Keyword(s):  
Taylor Polynomials

scholarly journals Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Main Question ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Taylor Polynomials

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.

scholarly journals Multivariate approximation by a combination of modified Taylor polynomials

2006 ◽  
Vol 196 (1) ◽  
pp. 162-179 ◽  
Author(s):  
Allal Guessab ◽  
Otheman Nouisser ◽  
Gerhard Schmeisser
Keyword(s):  
Multivariate Approximation ◽  
Taylor Polynomials

scholarly journals Hermite Subdivision Schemes and Taylor Polynomials

2008 ◽  
Vol 29 (2) ◽  
pp. 219-245 ◽  
Author(s):  
Serge Dubuc ◽  
Jean-Louis Merrien
Keyword(s):  
Subdivision Schemes ◽  
Taylor Polynomials ◽  
Hermite Subdivision

scholarly journals Computational Algorithm for Covariant Series Expansions in General Relativity

2018 ◽  
Vol 173 ◽  
pp. 03021 ◽  
Author(s):  
Ivan Potashov ◽  
Alexander Tsirulev
Keyword(s):  
Tensor Field ◽  
Computational Algorithm ◽  
Series Expansions ◽  
Tensor Fields ◽  
Normal Coordinates ◽  
Covariant Derivatives ◽  
Taylor Polynomials ◽  
Real Analytic ◽  
Derivatives Of ◽  
Torsion Free

We present a new algorithm for computing covariant power expansions of tensor fields in generalized Riemannian normal coordinates, introduced in some neighborhood of a parallelized k-dimensional submanifold (k = 0, 1, . . .< n; the case k = 0 corresponds to a point), by transforming the expansions to the corresponding Taylor series. For an arbitrary real analytic tensor field, the coefficients of such series are expressed in terms of its covariant derivatives and covariant derivatives of the curvature and the torsion. The algorithm computes the corresponding Taylor polynomials of arbitrary orders for the field components and is applicable to connections that are, in general, nonmetric and not torsion-free. We show that this computational problem belongs to the complexity class LEXP.

Taylor Polynomials and Difference Quotients

1979 ◽  
Vol 86 (8) ◽  
pp. 681
Author(s):  
Richard J. Bagby
Keyword(s):  
Taylor Polynomials ◽  
Difference Quotients
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