A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are
considered. It is named after Colin Maclaurin, who made extensive use of this special case of
Taylor series in the 18th century.
The Taylor series of a real or complex-valued function f
, that is infinitely differentiable at a
real or complex number a, is the power series
Here, m! denotes the factorial of m. The function f
denotes the mth derivative of f
evaluated at the point a. The derivative of order zero of f is defined to be f itself and
0 and 0! are both defined to be 1. With a = 0, the Maclaurin series takes the form:
This article is a derivative work of the creative commons share alike with attribution in
[1].
References
[1] Wikipedia contributors, “Taylor series,” Wikipedia, The Free Encyclopedia. Accessed
July 13, 2025.
[2] Kreyszig, E., “Advanced Engineering Mathematics.” Fifth Edition. John Wiley and
Sons, Inc. 1983.
