MacLaurin series

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)