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On the Type of Multiple Taylor Series and Random Taylor Series
2013It is studied that type of entire functions of multiple Taylor series and multiple random Taylor series. The characterization of type of entire functions of multiple Taylor series and multiple random Taylor series has obtained in terms of their Taylor’s series coefficients.
Wanchun Lu, Youhua Peng
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Taylor Polynomials and Taylor Series
2015Taylor polynomials are used to approximate values of functions at specified points. The error incurred is investigated by means of Taylor’s theorem. A method for ensuring that the approximation is accurate to within a specified error tolerance is illustrated. Taylor polynomials are then used to define Taylor series. Several techniques for finding these
Charles H. C. Little +2 more
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2020
This chapter focuses on the Taylor series. It points out that, Wwhen dealing with a complicated function, it can be useful to approximate the functionit with one of a simpler form. While the latter may not represent a complete and accurate description of the situation at hand, it frequently provides the only means of making analytical progress.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
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This chapter focuses on the Taylor series. It points out that, Wwhen dealing with a complicated function, it can be useful to approximate the functionit with one of a simpler form. While the latter may not represent a complete and accurate description of the situation at hand, it frequently provides the only means of making analytical progress.
D.S. Sivia, J.L. Rhodes, S.G. Rawlings
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2011
In this lecture, we shall prove Taylor’s Theorem, which expands a given analytic function in an infinite power series at each of its points of analyticity. The novelty of the proof comes from the fact that it requires only Cauchy’s integral formula for derivatives.
Ravi P. Agarwal +2 more
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In this lecture, we shall prove Taylor’s Theorem, which expands a given analytic function in an infinite power series at each of its points of analyticity. The novelty of the proof comes from the fact that it requires only Cauchy’s integral formula for derivatives.
Ravi P. Agarwal +2 more
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Taylor Series Numerical Integrator
2008 Second UKSIM European Symposium on Computer Modeling and Simulation, 2008The simulation language TKSL and modern Taylor series method has proved to be very powerful computing tools for extremely exact, stable and fast numerical solutions of systems of differential equations. In a natural way, TKSL also involves solutions of problems that can be reduced to solving a system of differential equations.
Michal Kraus 0001 +2 more
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Taylor Series in Control Theory
Tenth International Conference on Computer Modeling and Simulation (uksim 2008), 2008An original mathematical method which uses the Taylor series method for solving differential equations in a non-traditional way has been developed. Experimental calculations have shown and theoretical analyses have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving ...
Michal Kraus 0001 +3 more
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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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From Taylor series to Taylor models
AIP Conference Proceedings, 1997An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way.
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Series, Taylor — Maclaurin Series
1976By a series we mean a set of numbers a1, a2, a3… such that we have a rule for calculating a2, a3 etc. from the first number a1.Series occur in many problems in chemistry such as specific heats of solids, the theory of black-body radiation, solution of the Schrodinger equation, statistical thermodynamics and Fourier series in X-ray crystallography.
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