for a function
The power series
It was studied by C. MacLaurin . 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.
|||C. MacLaurin, "A treatise of fluxions" , 1–2 , Edinburgh (1742)|
MacLaurin series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=MacLaurin_series&oldid=15944