1

I made a code to display curves, here is the code:

\documentclass[12pt]{article}
\usepackage{pgfplots}
\usepackage{amsmath} 
\pgfplotsset{compat=1.18}
\usepackage{xcolor}
\begin{document}
\pgfplotstableread[col sep=comma]{
       -1.00000000e+00,  1.00000000e+00, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  7.35937500e+01, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  1.23005515e+02
       -5.78947368e-01,  1.00000000e+00, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  3.17518749e+01, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  5.91648918e+01
       -1.57894737e-01,  1.00000000e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  7.79163062e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  1.93708181e+01
        2.63157895e-01,  1.00000000e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -3.42580172e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -2.35859076e+00
        6.84210526e-01,  1.00000000e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -6.28491883e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -1.12508974e+01
        1.10526316e+00,  1.00000000e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -4.41589541e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -1.17793423e+01
        1.52631579e+00,  1.00000000e+00, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -6.94584190e-01, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -7.66284401e+00
        1.94736842e+00,  1.00000000e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00,  2.75748416e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00, -1.86599894e+00
        2.36842105e+00,  1.00000000e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  4.57310099e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  3.40091845e+00
        2.78947368e+00,  1.00000000e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  4.13937964e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  6.68195573e+00
        3.21052632e+00,  1.00000000e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  1.59775549e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  7.27548248e+00
        3.63157895e+00,  1.00000000e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00, -2.15601404e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00,  5.23419032e+00
        4.05263158e+00,  1.00000000e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00, -5.47184956e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00,  1.36509289e+00
        4.47368421e+00,  1.00000000e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -5.94534961e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -2.77047418e+00
        4.89473684e+00,  1.00000000e+00,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.17790734e-01,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.85685319e+00
        5.31578947e+00,  1.00000000e+00,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00,  1.50238725e+01,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00, -1.82406447e+00
        5.73684211e+00,  1.00000000e+00,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  4.50470077e+01,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  1.01521937e+01
        6.15789474e+00,  1.00000000e+00,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  9.50733043e+01,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  3.56505451e+01
        6.57894737e+00,  1.00000000e+00,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  1.71278774e+02,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  8.00039353e+01
        7.00000000e+00,  1.00000000e+00,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  2.80593750e+02,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  1.49299632e+02 
                
}\loadedtable
\begin{figure}[h]
\tikzset{ellipsenode/.style={draw, ellipse, thick, text width=5ex, align=center, inner sep=2pt}}
\begin{tikzpicture}
\begin{axis}[
axis lines=center,
xmin=-0.6,  xmax=6.6,
ymin=-17,  ymax=28,
axis on top,
xtick distance=1,
ytick distance=5,
tick label style={font=\footnotesize, inner sep=1pt, fill=white},
no marks, samples=15, smooth,
legend entries={
        $Q^{1/2,1/2,5}_{0}(x)$,
        $Q^{1/2,1/2,5}_{1}(x)$,
        $Q^{1/2,1/2,5}_{2}(x)$,
        $Q^{1/2,1/2,5}_{3}(x)$,
        $Q^{1/2,1/2,5}_{4}(x)$
},                ]
\addplot[color=red] table[x index=0,y index=1] {\loadedtable};
\addplot[color=blue]table[x index=0,y index=2] {\loadedtable};
\addplot[color=green] table[x index=0,y index=3] {\loadedtable};
\addplot[color=purple] table[x index=0,y index=4] {\loadedtable};
\addplot[color=yellow] table[x index=0,y index=5] {\loadedtable};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
axis lines=center,
xmin=-0.6,  xmax=6.6,
ymin=-17,  ymax=28,
axis on top,
xtick distance=1,
ytick distance=5,
tick label style={font=\footnotesize, inner sep=1pt, fill=white},
no marks, samples=15, smooth,
legend entries={
        $Q^{(3)}_{0}(x)$,
        $Q^{(3)}_{1}(x)$,
        $Q^{(3)}_{2}(x)$,
        $Q^{(3)}_{3}(x)$,
        $Q^{(3)}_{4}(x)$
},    
   ]
\addplot[color=red] table[x index=0,y index=1] {\loadedtable};
\addplot[color=blue]table[x index=0,y index=6] {\loadedtable};
\addplot[color=green] table[x index=0,y index=7] {\loadedtable};
\addplot[color=purple] table[x index=0,y index=8] {\loadedtable};
\addplot[color=yellow] table[x index=0,y index=9] {\loadedtable};
\end{axis}
\end{tikzpicture}
\caption{Graph of $Q^{1/2,1/2,5}_n$ and $Q^{(3)}_n$ for $n = 0, 1, 2, 3, 4$}
\end{figure}
\end{document}

Result

enter image description here

But in the compilation result, I want the two description tables to be small enough to see the graphs better. An idea please

1

2 Answers 2

1

Wrt. my comment with links here's a way to design or typeset your own legend. To better see the differences and to avoid clutter I put it as a separate answer.

result-smaller

Remarks

Preamble

For design it's better to use class standalone, as it adjusts to the "paper" size as needed. Package xcolor isn't needed here. We will need the tikzlibrary matrix to typeset the legend.

\documentclass[10pt,border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usepackage{amsmath} 
\pgfplotsset{compat=1.18}
%\usepackage{xcolor}    % <<< not needed in pgfplots
\usetikzlibrary{matrix} % <<< to typeset the legend, later

Plotset

It's obsolete, as we don't use the built-in legend.

%    \pgfplotsset{
%       every axis legend/.append style={
%           at={(1.02,1)},
%           anchor=north west,
%       },
%    }

Axis environment

  • let's put a title
  • remove all legend statements
  • add a \label AFTER each \addplot ... ;
  • define a \coordinate to use it later, here called (label)
    \begin{axis}[
        ...
        no marks, samples=15, smooth,
        title=$Q^{1/2,1/2,5}_n(x)$; % <<<
    ]
    % <<< new: put labels, to reference them later ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    \addplot[color=red] table[x index=0,y index=1] {\loadedtable};\label{plot:L1}
    ...
    
    % <<< new: legend will go here, in plot coordinates
    \coordinate (legend) at (.3,25);
    \end{axis}

Typeset your legend

The basic structure is \matrix[...] at (legend) { ... };, much like you'd do with a \node. You need to define some styles to see it the way you want it.

Think of \matrix as the Tikz-pendent to a Latex table. That's why you'll see the & & \\ structure for one row of data. Inside you just typeset as with regular text, referencing all those plot labels set earlier. As with all references, they need a second compile after introducing changes.

    % ~~~ building your legend using a matrix (it's like a table within Tikz) ~~~~
    \matrix[
        draw,               % to see it, with
        matrix of nodes,    % see manual
        anchor=north west,  % upper left corner
        font={\tiny},       % use smaller font, if you like
    ] at (legend) {
        Index $n$: &&\\
        \ref{plot:L1} 0&\ref{plot:L2} 1&\ref{plot:L3} 2\\
        \ref{plot:L4} 3&\ref{plot:L5} 4&\\
    };  

Result and code

result

\documentclass[10pt,border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usepackage{amsmath} 
\pgfplotsset{compat=1.18}
%\usepackage{xcolor}    % <<< not needed in pgfplots
\usetikzlibrary{matrix} % <<< to typeset the legend, later

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\begin{document}
    \pgfplotstableread[col sep=comma]{
           -1.00000000e+00,  1.00000000e+00, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  7.35937500e+01, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  1.23005515e+02
           -5.78947368e-01,  1.00000000e+00, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  3.17518749e+01, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  5.91648918e+01
           -1.57894737e-01,  1.00000000e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  7.79163062e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  1.93708181e+01
            2.63157895e-01,  1.00000000e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -3.42580172e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -2.35859076e+00
            6.84210526e-01,  1.00000000e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -6.28491883e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -1.12508974e+01
            1.10526316e+00,  1.00000000e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -4.41589541e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -1.17793423e+01
            1.52631579e+00,  1.00000000e+00, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -6.94584190e-01, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -7.66284401e+00
            1.94736842e+00,  1.00000000e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00,  2.75748416e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00, -1.86599894e+00
            2.36842105e+00,  1.00000000e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  4.57310099e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  3.40091845e+00
            2.78947368e+00,  1.00000000e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  4.13937964e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  6.68195573e+00
            3.21052632e+00,  1.00000000e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  1.59775549e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  7.27548248e+00
            3.63157895e+00,  1.00000000e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00, -2.15601404e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00,  5.23419032e+00
            4.05263158e+00,  1.00000000e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00, -5.47184956e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00,  1.36509289e+00
            4.47368421e+00,  1.00000000e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -5.94534961e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -2.77047418e+00
            4.89473684e+00,  1.00000000e+00,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.17790734e-01,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.85685319e+00
            5.31578947e+00,  1.00000000e+00,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00,  1.50238725e+01,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00, -1.82406447e+00
            5.73684211e+00,  1.00000000e+00,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  4.50470077e+01,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  1.01521937e+01
            6.15789474e+00,  1.00000000e+00,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  9.50733043e+01,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  3.56505451e+01
            6.57894737e+00,  1.00000000e+00,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  1.71278774e+02,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  8.00039353e+01
            7.00000000e+00,  1.00000000e+00,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  2.80593750e+02,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  1.49299632e+02 
                
}\loadedtable

\tikzset{
    ellipsenode/.style={
        draw, ellipse, thick, text width=5ex, 
        align=center, inner sep=2pt
    }
}

    \begin{tikzpicture}
%    \pgfplotsset{
%       every axis legend/.append style={
%           at={(1.02,1)},
%           anchor=north west,
%       },
%    }
    \begin{axis}[
        axis lines=center,
        xmin=-0.6,  xmax=6.6,
        ymin=-17,  ymax=28,
        axis on top,
        xtick distance=1,
        ytick distance=5,
        tick label style={font=\footnotesize, inner sep=1pt, fill=white},
        no marks, samples=15, smooth,
        title=$Q^{1/2,1/2,5}_n(x)$; % <<<
    ]
    % <<< new: put labels, to reference them later ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    \addplot[color=red] table[x index=0,y index=1] {\loadedtable};\label{plot:L1}
    \addplot[color=blue]table[x index=0,y index=2] {\loadedtable};\label{plot:L2}
    \addplot[color=green] table[x index=0,y index=3] {\loadedtable};\label{plot:L3}
    \addplot[color=purple] table[x index=0,y index=4] {\loadedtable};\label{plot:L4}
    \addplot[color=yellow] table[x index=0,y index=5] {\loadedtable};\label{plot:L5}
    
    % <<< new: legend will go here, in plot coordinates
    \coordinate (legend) at (.3,25);
    \end{axis}
    
    % ~~~ building your legend using a matrix (it's like a table within Tikz) ~~~~
    \matrix[
        draw,               % to see it, with
        matrix of nodes,    % see manual
        anchor=north west,  % upper left corner
        font={\tiny},       % use smaller font, if you like
    ] at (legend) {
        Index $n$: &&\\
        \ref{plot:L1} 0&\ref{plot:L2} 1&\ref{plot:L3} 2\\
        \ref{plot:L4} 3&\ref{plot:L5} 4&\\
    };  
    \end{tikzpicture}
\end{document}
1

Here is one way to do it. The easist thing would be to place the legend outside the drawing, say to the right. Ch. "4.9.5 Legend Appearance" (pdf) or "20.9 Legend Appearance" (html) describes it in the pgfplots-manual.

I tried putting the legend above, but it doesn't look nice. You could also Tikz-draw your own legend using the approach described on the first page of said chapter:

% from said chapter, sth. like this:
 \matrix [style=every axis legend] {
    draw plot specification 1 & \node{legend 1}\\
...

An other alternative might be to introduce abbreviations for your many function in your article, and use those with the plots. When they are shorter, the two drawings might fit as a 1-line drawing as you posted.

The difference to your code is this line of code, which I added to both of your plots:

  • specify the axis legend style
  • recall from the manual, that (0,0) is lower left, (1,1) upper right corner
  • place the legend slightly shifted to the upper right
  • anchor its upper left corner (north west) to said position
\begin{tikzpicture}
\pgfplotsset{                                 % <<<
    every axis legend/.append style={
        at={(1.02,1)},
        anchor=north west
    },
}
\begin{axis}[

result

% https://tex.stackexchange.com/questions/705129/using-legend-entries

\documentclass[12pt]{article}
\usepackage{pgfplots}
\usepackage{amsmath} 
\pgfplotsset{compat=1.18}
\usepackage{xcolor}
\begin{document}
\pgfplotstableread[col sep=comma]{
       -1.00000000e+00,  1.00000000e+00, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  7.35937500e+01, -3.50000000e+00,         9.75000000e+00, -2.62500000e+01,  1.23005515e+02
       -5.78947368e-01,  1.00000000e+00, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  3.17518749e+01, -3.07894737e+00,         6.97991690e+00, -1.45631652e+01,  5.91648918e+01
       -1.57894737e-01,  1.00000000e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  7.79163062e+00, -2.65789474e+00,         4.56440443e+00, -6.15144336e+00,  1.93708181e+01
        2.63157895e-01,  1.00000000e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -3.42580172e+00, -2.23684211e+00,         2.50346260e+00, -5.66955824e-01, -2.35859076e+00
        6.84210526e-01,  1.00000000e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -6.28491883e+00, -1.81578947e+00,         7.97091413e-01,  2.63817612e+00, -1.12508974e+01
        1.10526316e+00,  1.00000000e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -4.41589541e+00, -1.39473684e+00,        -5.54709141e-01,  3.91183117e+00, -1.17793423e+01
        1.52631579e+00,  1.00000000e+00, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -6.94584190e-01, -9.73684211e-01,        -1.55193906e+00,  3.70188803e+00, -7.66284401e+00
        1.94736842e+00,  1.00000000e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00,  2.75748416e+00, -5.52631579e-01,        -2.19459834e+00,  2.45622540e+00, -1.86599894e+00
        2.36842105e+00,  1.00000000e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  4.57310099e+00, -1.31578947e-01,        -2.48268698e+00,  6.22721971e-01,  3.40091845e+00
        2.78947368e+00,  1.00000000e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  4.13937964e+00,  2.89473684e-01,        -2.41620499e+00, -1.35074355e+00,  6.68195573e+00
        3.21052632e+00,  1.00000000e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  1.59775549e+00,  7.10526316e-01,        -1.99515235e+00, -3.01629246e+00,  7.27548248e+00
        3.63157895e+00,  1.00000000e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00, -2.15601404e+00,  1.13157895e+00,        -1.21952909e+00, -3.92604607e+00,  5.23419032e+00
        4.05263158e+00,  1.00000000e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00, -5.47184956e+00,  1.55263158e+00,        -8.93351801e-02, -3.63212567e+00,  1.36509289e+00
        4.47368421e+00,  1.00000000e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -5.94534961e+00,  1.97368421e+00,         1.39542936e+00, -1.68665257e+00, -2.77047418e+00
        4.89473684e+00,  1.00000000e+00,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.17790734e-01,  2.39473684e+00,         3.23476454e+00,  2.35825193e+00, -4.85685319e+00
        5.31578947e+00,  1.00000000e+00,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00,  1.50238725e+01,  2.81578947e+00,         5.42867036e+00,  8.95046654e+00, -1.82406447e+00
        5.73684211e+00,  1.00000000e+00,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  4.50470077e+01,  3.23684211e+00,         7.97714681e+00,  1.85378700e+01,  1.01521937e+01
        6.15789474e+00,  1.00000000e+00,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  9.50733043e+01,  3.65789474e+00,         1.08801939e+01,  3.15683409e+01,  3.56505451e+01
        6.57894737e+00,  1.00000000e+00,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  1.71278774e+02,  4.07894737e+00,         1.41378116e+01,  4.84897580e+01,  8.00039353e+01
        7.00000000e+00,  1.00000000e+00,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  2.80593750e+02,  4.50000000e+00,         1.77500000e+01,  6.97500000e+01,  1.49299632e+02 
                
}\loadedtable
\begin{figure}[h]
\tikzset{ellipsenode/.style={draw, ellipse, thick, text width=5ex, align=center, inner sep=2pt}}
\begin{tikzpicture}
\pgfplotsset{
    every axis legend/.append style={
        at={(1.02,1)},
        anchor=north west
    },
}
\begin{axis}[
axis lines=center,
xmin=-0.6,  xmax=6.6,
ymin=-17,  ymax=28,
axis on top,
xtick distance=1,
ytick distance=5,
tick label style={font=\footnotesize, inner sep=1pt, fill=white},
no marks, samples=15, smooth,
legend entries={
        $Q^{1/2,1/2,5}_{0}(x)$,
        $Q^{1/2,1/2,5}_{1}(x)$,
        $Q^{1/2,1/2,5}_{2}(x)$,
        $Q^{1/2,1/2,5}_{3}(x)$,
        $Q^{1/2,1/2,5}_{4}(x)$
},                ]
\addplot[color=red] table[x index=0,y index=1] {\loadedtable};
\addplot[color=blue]table[x index=0,y index=2] {\loadedtable};
\addplot[color=green] table[x index=0,y index=3] {\loadedtable};
\addplot[color=purple] table[x index=0,y index=4] {\loadedtable};
\addplot[color=yellow] table[x index=0,y index=5] {\loadedtable};
\end{axis}
\end{tikzpicture}
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~
\begin{tikzpicture}
\pgfplotsset{
    every axis legend/.append style={
        at={(1.02,1)},
        anchor=north west
    },
}
\begin{axis}[
axis lines=center,
xmin=-0.6,  xmax=6.6,
ymin=-17,  ymax=28,
axis on top,
xtick distance=1,
ytick distance=5,
tick label style={font=\footnotesize, inner sep=1pt, fill=white},
no marks, samples=15, smooth,
legend entries={
        $Q^{(3)}_{0}(x)$,
        $Q^{(3)}_{1}(x)$,
        $Q^{(3)}_{2}(x)$,
        $Q^{(3)}_{3}(x)$,
        $Q^{(3)}_{4}(x)$
},    
   ]
\addplot[color=red] table[x index=0,y index=1] {\loadedtable};
\addplot[color=blue]table[x index=0,y index=6] {\loadedtable};
\addplot[color=green] table[x index=0,y index=7] {\loadedtable};
\addplot[color=purple] table[x index=0,y index=8] {\loadedtable};
\addplot[color=yellow] table[x index=0,y index=9] {\loadedtable};
\end{axis}
\end{tikzpicture}
\caption{Graph of $Q^{1/2,1/2,5}_n$ and $Q^{(3)}_n$ for $n = 0, 1, 2, 3, 4$}
\end{figure}
\end{document}

P.S.:

For reference, this is what you get when moving the legends to the top of the plots:

result2

by using for both:

\pgfplotsset{
    every axis legend/.append style={
        at={(.5,1.03)},
        anchor=south
    },
}

P.S. 2

Here's an alternative using a title and focusing only on the relevant change: n. However, even listing only 0, 1, ... doesn't make the legend small enough here.

esult3

\begin{axis}[
    axis lines=center,
    xmin=-0.6,  xmax=6.6,
    ymin=-17,  ymax=28,
    axis on top,
    xtick distance=1,
    ytick distance=5,
    tick label style={font=\footnotesize, inner sep=1pt, fill=white},
    no marks, samples=15, smooth,
    legend entries={
            $n=0$,              % <<<
            $n=1$,
            $n=2$,
            $n=3$,
            $n=4$,
    },
    title=$Q^{1/2,1/2,5}_n(x)$; % <<<
]
1

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