plotting - Filling and Shading an Harmonic Curve

Suppose I have an equation plotted as shown:

Plot[(HarmonicNumber[K] - HarmonicNumber[K - r]) (HarmonicNumber[K] - 
 HarmonicNumber[-1 + r]) /. K -> 10, {r, 0, 11}, Filling -> 0.4]

But what I really want is to have the two (triangular?) filling FLIPPED inside at $x \approx2$ and $x \approx9$ . The direction of filling of the upper (semi-circular) part is not important. Preferably it can be Top/outside.

Can anybody help with this flipping?

Thanks

Answer

Another way, copying once more from @J.M.'s answer here: How can I fill under a function in a plot just to right of a specified vertical line?

Using @b.gatessucks definition of f:

f[r_, k_] = (HarmonicNumber[k] - HarmonicNumber[k - r]) (HarmonicNumber[k] - 
      HarmonicNumber[-1 + r])

we can do:

With[{ff = f[r, 10]}, 
   Plot[{ConditionalExpression[ff, ff < 0.4], 
         ConditionalExpression[ff, ff >= 0.4]}, {r, 0, 11}, 
   Filling -> {1 -> Axis, 2 -> Top}, PlotStyle -> ColorData[1, 1], 

   FillingStyle -> LightRed]]

based on the ideas linked above (using ConditionalExpression), getting the same result as in @b.gatessucks' answer.

The advantage of this approach is that you can easily modify the fillings (and other options) for the individual parts (but if you use a complicated function, I suspect it could turn slow (due to the added conditions)

Comments

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