3
$\begingroup$

By a hill function I mean a function such as $x^n/(K^n + x^n)$, where n is a real number smaller or greater than 1 up to around 10. Another way is to define a hill function is $\tanh((x/a)^n)$

I tried Expand on Wolfram|Alpha on x^1.2/(K^1.2+x^1.2) and it gave me an expansion of x about 1 (i.e., in terms of (x - 1)^i).

But in Mathematica I could not get the expansion.

Are there commands/packages other than Expand I can include for this purpose?

$\endgroup$
5
$\begingroup$
Series[x^1.2`/(K^1.2` + x^1.2`), {x, 1, 3}]

This expands your function about the point x=1 and gives 3 terms in the Taylor series.

In fact, if you type

expand x^1.2/(K^1.2+x^1.2) about 1

into Wolfram Alpha and then click the little button called "open code," it shows you something almost exactly like the Series expression above. Alternatively, you can type

= expand x^1.2/(K^1.2+x^1.2) about 1

into Mathematica. The = at the start of the line allows a much looser Wolfram-Alpha-like syntax. In this case, it again returns the same Series expression.

|improve this answer|||||
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.