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Computation and Application of Taylor Polynomials with Interval Remainder Bounds
Reliable Computing, 1998So-called Taylor models are used to determine guaranteed bounds of function values of multivalued and preferably complicated functions which are expansive to evaluate. A Taylor model of a function \(f\) consists of a Taylor polynomial of some convenient degree and an absolute error term in form of an interval. In order to determine the required bounds,
Martin Berz, Georg Hoffstätter
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Generalized Taylor’s Formula for Polynomials
2002In the ordinary calculus, a function, f(x) that possesses derivatives of all Orders is analytic at x = a if it can be expressed as a power series about x = a. Taylor’s theorem teils us the power series is $$ f(x) = \sum\limits_{n = 0}^\infty {f^{(n)} (a)} \frac{{(x - a)^n }} {{n!}}.
Victor Kac, Pokman Cheung
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Taylor Polynomials for Rational Functions
The College Mathematics Journal, 1998(1998). Taylor Polynomials for Rational Functions. The College Mathematics Journal: Vol. 29, No. 3, pp. 226-228.
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ON THE GALOIS GROUPS OF THE EXPONENTIAL TAYLOR POLYNOMIALS
1987Let \(f_ n(X)\) be the polynomial \(1+x+x^ 2/2!+\dots+x^ n/n!\) over \({\mathbb{Q}}\). Then [cf. \textit{I. Schur}, Sitzungsber. Akad. Wiss. Berlin 1930, 443--449 (1930; JFM 56.0110.02)] the Galois group of \(f_ n(X)\) is the alternating group \(A_ n\) if 4 divides \(n\) and it is equal to the symmetric group \(S_ n\) otherwise.
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Polynomial inequalities and universal Taylor series
Mathematische Zeitschrift, 2016For a compact set \(K\) in the complex plane, let \(C(K)\) denote the space of continuous functions on \(K\) endowed with the uniform norm. A Taylor series \(\sum_{j \geq 0} a_j z^j\) of a function \(f\) holomorphic in the open unit disk is called universal if for all compact sets \(K\) outside the closed unit disk with connected complement the partial
Mouze, Augustin, Munnier, Vincent
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Taylor polynomial solutions of Volterra integral equations
International Journal of Mathematical Education in Science and Technology, 1994The method of Kanwal and Liu for the solution of Fredholm integral equations is applied to certain linear and nonlinear Volterra integral equations of the second kind. Some equations considered by other authors are solved in terms of Taylor polynomials and the results are compared.
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Generalized Taylor polynomials for axisymmetric plates and shells
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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