I’m trying to reproduce some plots from the analytical expression:

$f(xi)=left(frac{2}{beta^2}-1right)+left(frac{theta,e^{-beta}}{2}-frac{1}{2}right)xi+sum_{n=1}^{60}left(frac{(-beta)^n}{n!}xi^{1+n/2}zeta_Hleft(-frac{n}{2},1+frac{1}{xi}right)right)$.

I need to plot $f(-4x)$ for several values of $beta$ and with $theta=0$ and $theta=1$. In the attached picture, the left panel is what I have to get (ignore the blue curves), but Mathematica gives me a lot of noise.

My code is:

```
f((Beta)_, (Xi)_,M_, (Theta)_) := ((2/(Beta)^2 -1) + (((Theta) Exp(-(Beta)))/2 - 1/2) (Xi) + Sum(((-(Beta))^n (Xi)^(1 + n/2))/n! HurwitzZeta(-(n/2), 1 + 1/(Xi)), {n, 1, M}));
Plot({f(0.5, -4 x, 60, 1), f(0.5, 4 x, 60, 0),
f(0.8, -4 x, 60, 1), f(0.8, 4 x, 60, 0), f(1.1, -4 x, 60, 1),
f(1.1, 4 x, 60, 0)}, {x, -6, 6}, AxesOrigin -> {0, 0},
PlotStyle -> {Green, Green, Red, Red, Black, Black},
PlotRange -> {0, 8})
```

Do you have an idea of what is going on?

Thanks!