= Siegel–Shidlovsky theorem
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= Siegel–Shidlovskii theorem
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{synonym}
Let a vector of <E-functions> satisfy $f'=A(z)f$ with $A\in\operatorname{Mat}_s(\overline{\mathbb Q}(z))$. At a nonzero algebraic point $\xi$ which is not a pole of $A$, the transcendence degree of the values over $\overline{\mathbb Q}$ equals the transcendence degree of the functions over $\overline{\mathbb Q}(z)$. In particular algebraically independent functions give algebraically independent values. The exponential system $f_j=e^{\gamma_jz}$, for rationally independent algebraic $\gamma_j$, recovers the <Lindemann–Weierstrass theorem> by evaluating at one.
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