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title: "Taylor series"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574961/Taylor%20series"
format: markdown
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The Taylor series is a formula that determines a polynomial approximation in *x* of some mathematical function *f(x)* centered at some value *x*<sub>*0*</sub>:

![image](media://421bbddf-a624-4437-b628-7ec6ee889071)

> Macro (mathblock)


where *f*<sup>*(m)*</sup> represents the *m*<sup>th</sup> derivative with respect to *x* of the function *f*.


In the special case where *x*<sub>*0*</sub> = 0, the series is known as the *Maclaurin series* of *f(x)*:

![image](media://04cc5f4b-f176-400b-a0b3-5cbf8c08c76f)

> Macro (mathblock)


The Taylor and Maclaurin series expansions are used elsewhere in ModelAssist to provide polynomial approximations to probability distribution functions.




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