MacLaurin series

From Encyclopedia of Mathematics
Revision as of 17:14, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

for a function

The power series

It was studied by C. MacLaurin [1]. If a function analytic at zero is expanded as a power series around zero, then this series coincides with the MacLaurin series. When a function depends on variables, the MacLaurin series is a multiple power series:

in which the summation is over the multi-indices , , and are non-negative integers. A MacLaurin series is a special case of a Taylor series.


[1] C. MacLaurin, "A treatise of fluxions" , 1–2 , Edinburgh (1742)
How to Cite This Entry:
MacLaurin series. 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