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 (3.00000,4.50000) {LINEAR EQUATION};
3 \node[] at (9.30000,4.50000) {LOGARITHMIC DERIVATIVE};
4 \node[] at (3.00000,3.25000) {$D_2^{\prime\prime}=-D_2$};
5 \node[] at (9.30000,3.25000) {$T_2^{\prime}=1+T_2^2$};
6 \node[] at (3.00000,1.85000) {$D_3^{\prime\prime\prime}=-D_3$};
7 \node[] at (9.30000,1.85000) {$T_3^{\prime\prime}-3T_3T_3^{\prime}+T_3^3=1$};
8 \node[] at (6.15000,0.50000) {$T_N=-D_N^{\prime}/D_N\quad\text{only where }D_N\ne0$};
9 \draw[black!25] (6.10000,1.10000) -- (6.10000,4.65000);
10 \node[] at (6.10000,-0.40000) {$T_4(z)=\frac{z^3}{3!}+34\frac{z^7}{7!}+\cdots$};
11 \end{tikzpicture}

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