Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[] at (6.40000,4.50000) {$N=3,\ j=1,\ n=2:\quad 7!=1!\,3^6\,2!\,(2/3)_2(4/3)_2$};
3 \draw[fill=black!0,draw=black!40,line width=.35pt] (0.80000,3.15000) rectangle ++(1.60000,0.70000);
4 \node[] at (1.60000,3.50000) {$\frac{2}{3}$};
5 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.40000,3.15000) rectangle ++(1.60000,0.70000);
6 \node[] at (3.20000,3.50000) {$\frac{5}{3}$};
7 \node[anchor=west] at (4.50000,3.50000) {$(2/3)_2$};
8 \draw[fill=black!20,draw=black!40,line width=.35pt] (0.80000,2.25000) rectangle ++(1.60000,0.70000);
9 \node[] at (1.60000,2.60000) {$1$};
10 \draw[fill=black!20,draw=black!40,line width=.35pt] (2.40000,2.25000) rectangle ++(1.60000,0.70000);
11 \node[] at (3.20000,2.60000) {$2$};
12 \node[anchor=west] at (4.50000,2.60000) {$(1)_2=2!$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt] (0.80000,1.35000) rectangle ++(1.60000,0.70000);
14 \node[] at (1.60000,1.70000) {$\frac{4}{3}$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.40000,1.35000) rectangle ++(1.60000,0.70000);
16 \node[] at (3.20000,1.70000) {$\frac{7}{3}$};
17 \node[anchor=west] at (4.50000,1.70000) {$(4/3)_2$};
18 \node[] at (9.30000,3.30000) {$A_{3,1}=\{2/3,4/3\}$};
19 \node[] at (9.30000,2.00000) {$\displaystyle E_{3,1}(z)=z\,{}_0F_2\!\left(;\frac23,\frac43;\frac{z^3}{27}\right)$};
20 \node[] at (6.30000,-0.05000) {The omitted unit parameter is already the hypergeometric $n!$.};
21 \end{tikzpicture}

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