# IJPAM: Volume 86, No. 1 (2013)

A NOTE ON TWO POINT TAYLOR EXPANSION II

Kazuaki Kitahara1, Takako Yamada2, Kazuki Fujiwara3
1,3School of Science and Technology
Kwansei Gakuin University
Sanda, 669-1337, JAPAN
2School of Policy Studies
Kwansei Gakuin University
Sanda, 669-1337, JAPAN

Abstract. Let be a continuous function on , the function restricted to the subinterval and the function restricted to the subinterval . If is expressed as the Taylor expansion of about , then we show that is expressed as the two point Taylor expansion about on the interval . Furthermore, the -th order derivatives of on are expressed as the termwise times differentiation of the two point Taylor expansion about .

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

Key Words and Phrases: Hermite interpolation, Taylor expansion, termwise differentiation