MacLaurin formula

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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.


For some expressions for the remainder and for estimates of it see Taylor formula.


[a1] W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1976) pp. 107–108
How to Cite This Entry:
MacLaurin formula. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article