How to have displaystyle in pgfplots' legend?

Question

I want the legend of my plot to display a fraction the same way it would be done using displaystyle. When using displaystyle, the border of the legend gets cut (see picture below). How can I proceed to nicely format my equation ? 
I have tried using addlegendentryextended but it doesn't work.

Here is a MWE :

documentclass{article}
usepackage{tikz}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}

begin{tikzpicture}
    begin{axis}[axis x line=center,
      axis y line=center,
        legend pos = north west,
        xlabel = $x$,
        ylabel = {$f(x)$},
        xmin=-5,
        xmax=5,
        ymin=-2,
        ymax=5,
    ]
    %Below the red parabola is defined
    addplot [
        samples=100,
        color=blue,
    ]
    {e^x};
    addlegendentry{$e^x$}

%Here the blue parabloa is defined
    addplot [
        domain=-4:5,
        samples=100,
        color=red,
        ]
        {1+x};
    addlegendentry{$1+x$}

addplot [
        domain=-3:5,
        samples=100,
        color=orange,
    ]
    {1+ x + 1/2*x^2};
    addlegendentry{$displaystyle 1+ x +frac{1}{2}x^2$} % <---- goes out of border

end{axis}
end{tikzpicture}
end{document}

Here is the output :

Leone · Answer

Update: I did some further research and found that this problem has already been solved here. I've just faced the same problem and solved it using raisebox: raisebox{}{} The drawback of doing this is the necessity of manually tuning the So, for your problem: documentclass{article} usepackage{tikz} usepackage{pgfplots} pgfplotsset{compat=1.16} begin{document} begin{tikzpicture} begin{axis}[axis x line=center, axis y line=center, legend pos = north west, xlabel = $x$, ylabel = {$f(x)$}, xmin=-5, xmax=5, ymin=-2, ymax=5, ] %Below the red parabola is defined addplot [ samples=100, color=blue, ] {e^x}; addlegendentry{$e^x$} %Here the blue parabloa is defined addplot [ domain=-4:5, samples=100, color=red, ] {1+x}; addlegendentry{$1+x$} addplot [ domain=-3:5, samples=100, color=orange, ] {1+ x + 1/2*x^2}; addlegendentry{raisebox{7pt}{$displaystyle 1+ x +frac{1}{2}x^2$}} % <---- goes out of border end{axis} end{tikzpicture} end{document}

How to have displaystyle in pgfplots' legend?

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