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Lindemann–Weierstrass theorem
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==Naming convention== The theorem is also known variously as the '''Hermite–Lindemann theorem''' and the '''Hermite–Lindemann–Weierstrass theorem'''. [[Charles Hermite]] first proved the simpler theorem where the {{math|α<sub>''i''</sub>}} exponents are required to be [[rational integer]]s and linear independence is only assured over the rational integers,<ref>{{Harvnb|Hermite|1873|pp=18–24}}.</ref><ref>{{Harvnb|Hermite|1874}}</ref> a result sometimes referred to as Hermite's theorem.<ref>{{Harvnb|Gelfond|2015}}.</ref> Although that appears to be a special case of the above theorem, the general result can be reduced to this simpler case. Lindemann was the first to allow algebraic numbers into Hermite's work in 1882.<ref name="Lindemann1882a">{{Harvnb|Lindemann|1882a}}, {{Harvnb|Lindemann|1882b}}.</ref> Shortly afterwards Weierstrass obtained the full result,<ref name="Weierstrass1885">{{Harvnb|Weierstrass|1885|pp=1067–1086}},</ref> and further simplifications have been made by several mathematicians, most notably by [[David Hilbert]]<ref>{{Harvnb|Hilbert|1893|pp=216–219}}.</ref> and [[Paul Gordan]].<ref>{{Harvnb|Gordan|1893|pp=222–224}}.</ref>
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