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KS update 1.3
:<math> \sum_{n=0} ^ {\infin } \frac {f^{(n)}(a)}{n!} \, (x-a)^{n}</math>
:<math> \sum_{n=0} ^ {\infin } \frac {f^{(n)}(a)}{n!} \, (x-a)^{n}</math>
Here ''n''! is the [[factorial]] of ''n''. ''ƒ''<sup> (''n'')</sup>(''a'') is the ''n''th [[derivative]] of ''ƒ'' at the point ''a''. <math>a</math> is a number in the function's [[domain]]. If the Taylor Series of a function is equal to that function, the function is called an "[[analytic]] function."
Here ''n''! is the [[factorial]] of ''n''. ''ƒ''<sup> (''n'')</sup>(''a'') is the ''n''th [[derivative]] of ''ƒ'' at the point ''a''. <math>a</math> is a number in the function's [[domain]]. If the Taylor Series of a function is equal to that function, the function is called an "Analytic function"[https://en.wikipedia.org/wiki/Analytic_function].
== Maclaurin series ==
== Maclaurin series ==
When <math>a=0</math>, the function is called a '''Maclaurin series'''. The Maclaurin series written as a [[power series]] looks like:
When <math>a=0</math>, the function is called a '''Maclaurin series'''. The Maclaurin series written as a [[power series]] looks like: