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General Information
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2014Vol.4(4): 287-291 ISSN: 2010-3697
DOI: 10.7763/IJMO.2014.V4.387

A Note on Two Point Taylor Expansion III

Kazuaki Kitahara and Taka-Aki Okuno

Abstract—If a function is analytic on an interval, then the function is expressed as the Taylor expansion about a point in the interval. Furthermore, possibility of Taylor expansions of functions about two or three points has also been studying as useful expressions in several fields of mathematical sciences. In this paper, we show the following main result by estimating values of divided differences: Let f is a polynomial p on the interval [├ 1⁄3,∞) ┤ and f is a polynomial q on the interval (├ -∞,1⁄3] ┤. Then, we show that f is expressed as the two point Taylor expansion about -1,1 with the multiplicity weight (2,1) on the interval (α,β), where α is the solution of (x+1)^2 (x-1)=-32⁄27 with α<-1 and β is the solution of (x+1)^2 (x-1)=32⁄27 with β>1.
Index Terms—Polynomial interpolation, Hermite interpolation, Taylor expansion, two point taylor expansion.

The authors are with the School of Science and Technology, Kwansei Gakuin University, Japan (e-mail: kitahara@kwansei.ac.jp).


Cite: Kazuaki Kitahara and Taka-Aki Okuno, "A Note on Two Point Taylor Expansion III," International Journal of Modeling and Optimization vol. 4, no. 4, pp. 95-99, 2014.

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