How to bend a mathematical formula around an arc or circle

Question

i would like to bend a math formula around a circle. While it is working with text, LaTeX would not bend a formula in a math environment around a circle, at least, i hadn´t had success. The following code i wrote for a test:

\documentclass[convert={density=300,size=1080x800,outext=.png}]{standalone}
\usepackage{fontspec}
\usepackage{amssymb}
\usepackage{unicode-math}
\usepackage{xfrac}
\usepackage{tikz}
\usepackage{calc}
\usetikzlibrary{decorations.text,fit,chains,calc,shapes.geometric,intersections}
\usepackage[margin=15mm]{geometry}

\begin{document}
\begin{tikzpicture}
\begin{scope}[shift={(0cm,0cm)}, fill opacity=0.5, mytext/.style={text  opacity=1,font=\large\bfseries}]
% Kreise  
\draw[fill=red, draw = black] (0,0) circle (5); % Complex Numbers
\draw[fill=blue!10, draw = black,name path=circle 2] (0,0) circle (4.2);  % Imaginary Numbers
\end{scope}

\draw [ draw opacity=0.1, rotate=120,
   postaction={decorate, decoration={raise=-1ex,text along path,reverse path,text align={fit to path stretching spaces},
              text={|\ttfamily\huge\color{blue}|Outer\space Space       \space}}}] (0,0) circle (4.6cm);
\draw [draw opacity=0.1, rotate=180,
   postaction={ decorate, decoration={raise=-1ex,text along path,reverse path,text align={fit to path stretching spaces},
       text={|\ttfamily\huge\color{green}|Inner\space Space \space}}}] (0,0) circle (3.8cm);

\node at (4,0) (N) {\tiny 1,2,3,4};
\node[rotate=90] at (-3,1) (N) {$y(n)=h_0x(n)+h_1x(n-1)+\dots +h_{N-1}x(n-N+1)=\sum_{k=0}^{N-1}h_kx(n-k)$};
\end{tikzpicture}

\end{document}

The following result is generated, but the math formular is not bended.

Answer 1

From the Manual !

• It is only possible to typeset text in math mode under considerable restrictions. Math mode is entered and exited using any character of category code 3 (e.g., in plain TEX this is $). Math subscripts and superscripts need to be contained within braces (e.g., {^y_i}) as do commands like \times or \cdot. However, even modestly complex mathematical typesetting is unlikely to be successful along a path (or even desirable).

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.text}

\begin{document}

\begin{tikzpicture}[decoration={text along path, text={$\ \ \ y(n)={h_0}x(n)+{h_1}x(n-1)+{\ldots} +{h_{N-1}}x(n-N+1)={\sum_{k=0}^{N-1}}{h_kx(n-k)}$}}]
  \path [decorate]
    (0,0) .. controls (0,6) and (9,6) .. (9,0);
\end{tikzpicture}
\end{document}

Update

\documentclass[margin=1cm]{standalone}
\usepackage{fontspec}
\usepackage{amssymb}
\usepackage{unicode-math}
\usepackage{xfrac}
\usepackage{tikz}
\usepackage{calc}
\usetikzlibrary{decorations.text,fit,chains,calc,shapes.geometric,intersections}

\begin{document}

\begin{tikzpicture}[
disk 1/.style={fill=red, draw = black},
disk 2/.style={fill=blue!10, draw = black,name path=circle 2},
disk 3/.style={
    rotate  = -90,
    postaction  = %
                 {decorate, 
                  decoration={raise = -1ex,
                              text along path,
                              reverse path,
                              text align = {fit to path stretching spaces},
                              text = {|\ttfamily\huge\color{blue}|
                                       Outer\space Space \space}}}},
disk 4/.style={
   draw opacity=0.1, 
   rotate=15,
   postaction={decorate,
               decoration={
                         raise=-1ex,
                         text along path,
                         reverse path,
                         text align={fit to path stretching spaces},
                         text={%
            |\color{red}| $y(n)={h_0}x(n)+{h_1}x(n-1)+{\cdots}+%
               {h_{N-1}}x(n-N+1)={\sum_{k=0}^{N-1}}{h_k}x(n-k)$ }
                              }
                        }
                }
    ]
\begin{scope}[  mytext/.style={text  opacity=1,
                font=\large\bfseries}]
% Disk 1
\draw[disk 1] (0,0) circle (5); 

% Disk 2
\draw[disk 2] (0,0) circle (4.2);
\end{scope}

% Disk 3
\path[disk 3] (0,0) circle (4.6cm);

% Disk 4
 \path[disk 4] (0,0) circle (3.8cm); 

\end{tikzpicture}
\end{document}