recursive functions in pgfplots using 'declare function'

Question

I would like to use pgfplots to create a figure where I plot curves that have a recursive formula. I tried a very simple case that uses the declare function command to see whether this is possible, and I can't compile (TeX capacity exceeded). Is it even possible to do this?

\documentclass{standalone}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}[
  declare function={test(\p)=ifthenelse(\p>1, test(\p-1), 0.5);},
]
    \begin{axis}[]
    % use TeX as calculator:
    \addplot [mark=none] {x};
    \addplot [mark=none] {test(0)};
    \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

As marmot already stated in the comment below the question you can use the tikzmath library to declare recursive functions. Instead of declare function you simply use evaluate and than you have to use a little bit different syntax. But I think with the Fibonacci example from the pgfmanual (section 56.1 on page 640 of v3.0.1a) you will be able to modify it to your needs.

% used PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}[
    evaluate={
        % (copied from the pgfmanual)
        % Adapted from http://www.cs.northwestern.edu/academics/courses/110/html/fib_rec.html
        function fibonacci(\n) {
            if \n == 0 then {
                return 0;
            } else {
                return fibonacci2(\n, 0, 1);
            };
        };
        function fibonacci2(\n, \p, \q) {
            if \n == 1 then {
                return \q;
            } else {
                return fibonacci2(\n-1, \q, \p+\q);
            };
        };
    },
]
    \begin{axis}
        \addplot+ [domain=0:10,samples=11] {fibonacci(x)};
    \end{axis}
\end{tikzpicture}
\end{document}