# MacLaurin series

From Encyclopedia of Mathematics

*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.

#### References

[1] | C. MacLaurin, "A treatise of fluxions" , 1–2 , Edinburgh (1742) |

**How to Cite This Entry:**

MacLaurin series.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=MacLaurin_series&oldid=15944

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