Plotting the percentage difference between two curves

Question

I would like to plot the percentage difference between the following functions:

Q5[x_] := Abs[Re[(1 - x)^(5/2) Hypergeometric2F1[-5/2, 1/2, 3/2, 3 x/(x - 1)]]]
q5[x_] := Series[Q5[x], {x, 0, 3}]

I simply do the following:

error[x_] := Abs[Q5[x] - q5[x]]
Plot[error[x], {x, 0, 2}]

I was hoping to obtain the plot:

Answer 1

Since Re and Abs are not differentiable, it is better to find the series expansion before using them. So:

iQ5[x_] := (1 - x)^(5/2) Hypergeometric2F1[-5/2, 1/2, 3/2, 3 x/(x - 1)]
Q5[x_] := Abs @ Re @ iQ5[x]
q5[x_] = Abs @ Re @ Normal @ Series[iQ5[x], {x, 0, 3}]

Abs[1 + Re[(3 x^2)/2 + x^3/7]]

To get the percentage error you need to divide the difference by the expected value and multiply by 100:

percentError[x_] := 100 Abs[Q5[x] - q5[x]]/Q5[x]

Visualization:

Plot[percentError[x], {x, 0, 2}, Exclusions->1]