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
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
.
Received: March 3, 2013
AMS Subject Classification: 41A10, 41A05, 41A58
Key Words and Phrases: Hermite interpolation, Taylor expansion, termwise differentiation
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DOI: 10.12732/ijpam.v86i1.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 1