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# Maclaurin & Taylor Series

### Taylor Series

From the [Wikipedia](https://en.wikipedia.org/wiki/Taylor_series):

"In [mathematics](https://en.wikipedia.org/wiki/Mathematics),  the **Taylor series** of a [function](https://en.wikipedia.org/wiki/Function_\(mathematics\)) is an [infinite sum](https://en.wikipedia.org/wiki/Series_\(mathematics\)) of terms that are expressed in terms of the function's [derivatives](https://en.wikipedia.org/wiki/Derivative) at a single point."

$$\large g(x) = \sum\limits\_{n=0}^{\infty} \frac{f^{(n)}(p)}{n!}(x-p)^n$$

### Maclaurin Series

A Taylor series expansion of a function about 0

$$\large g(x) = \sum\limits\_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!}x^n$$