# 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=15362

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article