Plot a function with multiple parameters usign TiKz

Question

I need to graph a function that have multiple given parameters:

EDIT

The code is almost done but I have a little and tricky problem, the solid line is supposed to start at y=3 (just as the dashed one), and now is just a little bit above of 3. This is my figure:

And this is the expected one:

I have reviewed the code for many hours but I cannot find the error that generates that difference that for me is too important, can any one help me please? This is my code:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots} 
\pgfplotsset{compat=1.17} 
\pgfplotsset{every non boxed x axis/.append style={x axis line style=-},
     every non boxed y axis/.append style={y axis line style=-}}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture} 
\begin{axis}[xlabel={signal},
            ylabel={equilibrium bid},
            axis lines=left,
            declare function={H(\x,\n,\a,\b,\R)=
            pow(\R,(\b*(\n-1)+1))*%0
            pow(((\n*\b)+\a-1),(\b*(\n-1)))*%0
            pow(((\n*\b)+\a),(-\b*(\n-1)))*%0
            pow((\x),(-\b*(\n-1)))+(((\n*\b)+\a)/((\n*\b)+\a-1))*\x*%1
            ((\n-1)*\b)/((((\n-1)*\b)+1))*%0
            (1-pow(\R,((\b*(\n-1))+1))*%1
            pow(((\n*\b)+\a-1),(\b*(\n-1)+1))*%0
            pow(((\n*\b)+\a),((-\b*(\n-1))-1))*%0
            pow((\x),((-\b*(\n-1))-1)));},%-1
            domain=2.1:2.7,no marks,samples=11
            ,smooth, ytick distance=0.01, ymin=2.995, ymax=3.055, xmin=2.1, xmax=2.7] 
 \addplot[color=black, domain=2.1429:2.7]{H(x,2,2.5,0.5,3)}; 
 \addplot[color=black, dashed, domain=2.25:2.7]{H(x,3,2.5,0.5,3)}; 
\end{axis} 
\end{tikzpicture}
\end{figure}
\end{document}

I have checked parentheses and multiplication signs many times and really can't find my mistake.

I appreciate any advice or modification because I really need to come up with that result. The function formula is at the beginning of the post and maybe there is an error there but I am not able to find it.

Answer 1

You can define functions of several variables, and take one of them (or a combination thereof) to be the plot variable, just like in any (other) computer algebra system. I was not motivated to type in your full function but "only" the first term, but this is more than enough to illustrate the point.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[declare function={H(\x,\n,\a,\b,\R)=pow(\R,\b*(\n-1)+1)*
pow(\n*\b+\a-1,\b*(\n-1))*pow(\n*\b+\a,-\b*(\n-1))*pow(\x,-\b*(\n-1));},
    domain=2:2.7,no marks]
 \addplot{H(x,2,2.5,0.5,3)};
 \addplot[color=red]{H(x,2,2.5,0.5,4)};
\end{axis}
\end{tikzpicture}
\end{document}

As you see, in the second plot the parameter 3 was changed to 4.

ADDENDUM: As for the code from your comment, this works if you add the missing multiplication signs. E.g. \b(\n-1) needs to become \b*(\n-1).

\documentclass[tikz,border=3mm]{standalone} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.17} 
\begin{document} 
\begin{tikzpicture} 
\begin{axis}[declare function={H(\x,\n,\a,\b,\R)=pow(\R,\b*(\n-1)+1)*% 
  pow(\n*\b+\a-1,\b*(\n-1))*pow(\n*\b+\a,-\b*(\n-1))*pow(\x,-\b*(\n-1))+%
  (\n*\b+\a)/(\n*\b+\a-1)*\x*(((\n-1)*\b)/((\n-1)*\b+1))*%
  (1-pow(\R,\b*(\n-1)+1)*pow(\n*\b+\a-1,\b*(\n-1)+1)*%
  pow(\n*\b+\a,-\b*(\n-1)-1)*%
  pow(\x,-\b*(\n-1)-1));},
  domain=2.1:2.7,no marks,samples=11,smooth] 
 \addplot[color=black]{H(x,2,2.5,0.5,3)}; 
 \addplot[color=red]{H(x,2,2.5,0.6,3)}; 
\end{axis} 
\end{tikzpicture} 
\end{document} 

One should add that this function is perhaps already beyond what one could reasonably do with pgfplots alone. If you increase the samples you will see why.

Answer 2

If I may, I'd like to complete @Schrodingerscat with a useful trick (he taught me).

When you want to draw a function with less than 9 parameters you want to play with, wrap your tikzpicture in a \newcommand :

\documentclass[tikz,export]{standalone}
% convert -density 300 -delay 12 -loop 0 -alpha remove MyGraph.pdf MyGraph.gif 
\usepackage{animate}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\tikzset{
    declare function={
    H(\x,\n,\a,\b,\R)= pow(\R,\b*(\n-1)+1)*
                       pow(\n*\b+\a-1,\b*(\n-1))*
                       pow(\n*\b+\a,-\b*(\n-1))*
                       pow(\x,-\b*(\n-1));}}

\newcommand{\MyGraphWithParameters}[4]{
%   \def\ParOne{#1}
%   \def\ParTwo{#2}
%   \def\ParThree{#3}
%   \def\ParFour{#4}

    \begin{axis}[domain=2:2.7,no marks,clip=true, ymin=1,ymax=5]
%   \addplot{H(x,\ParOne,\ParTwo,\ParThree,\ParFour)};
    \addplot{H(x,#1,#2,#3,#4)};
    \addplot[color=red]{H(x,2,2.5,0.5,4)};  
    \end{axis}
}

\begin{document}
\foreach \i in {1,...,10}   %each will be an independant frame in pdf you can call with `\includegraphics{}`
{\begin{tikzpicture}
    \MyGraphWithParameters{\i}{2.5}{0.5}{3}
\end{tikzpicture}
}
\end{document}

You can then create easily animations or gifs as explained here