= Addition closure of Siegel E-functions
{title2=$f,g\in\mathcal E\Longrightarrow f+g\in\mathcal E$}
Work in the <compositum> of the two coefficient fields. Conjugate coefficient bounds add, while multiplying the common denominators clears both coefficient lists. For Siegel's original bounds $O_\epsilon(n^{\epsilon n})$, use $\epsilon/2$ in each denominator estimate. A nonzero <linear differential equation> for the sum follows because its derivatives lie in the sum of the two finite-dimensional derivative spaces over the <rational function> <field>. The stricter exponential arithmetic bounds are preserved as well.
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