IJPAM: Volume 75, No. 3 (2012)

A NOTE ON TWO POINT TAYLOR EXPANSION

Kazuaki Kitahara$^1$, Taizo Chiyonobu$^2$, Hirokazu Tsukamoto$^3$
$^{1,2,3}$School of Science and Technology
Kwansei Gakuin University
Sanda, 669-1337, JAPAN


Abstract. Let $f$ be a piecewise polynomial continuous function such that $f$ is a polynomial $p$ on the interval $[0, \infty)$ and $f$ is a polynomial $q$ on the interval $(-\infty, 0]$. Then, we show that $f$ is expressed as the two point Taylor expansion about $-1, 1$ on the interval $(-\sqrt{2}, \sqrt{2})$.

Received: October 8, 2011

AMS Subject Classification: 41A10, 41A05, 41A58

Key Words and Phrases: Hermite interpolation, Taylor expansion

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 75
Issue: 3