MacLaurin formula
From Encyclopedia of Mathematics
A particular case of the Taylor formula. Let a function 
have 
derivatives at 
. Then in some neighbourhood 
of this point 
can be represented in the form
 |
where 
, the 
-th order remainder term, can be represented in some form or other.
The term "MacLaurin formula" is also used for functions of 
variables 
. In this case 
in the MacLaurin formula is taken to be a multi-index, 
(see MacLaurin series). The formula is named after C. MacLaurin.
Comments
For some expressions for the remainder 
and for estimates of it see Taylor formula.
References
| [a1] | W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1976) pp. 107–108 |
How to Cite This Entry:
MacLaurin formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=MacLaurin_formula&oldid=47742
MacLaurin formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=MacLaurin_formula&oldid=47742
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article