How do I prove this? I've tried to search it by the name of "Hermite-Lindemann's" theorem but I don't find anything. If someone has a reference link or something, i would appreciate it.
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I don't know, but could this be helpful? $\longrightarrow$ https://math.stackexchange.com/questions/186752/proof-that-ex-is-a-transcendental-function-of-x – Mr Pie Dec 12 '17 at 00:51
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1This is a special case of the Lindemann-Weierstrass Theorem. – lulu Dec 12 '17 at 00:53
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More specifically, this is Lindemann's theorem. – Robert Israel Dec 12 '17 at 00:56
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@RobertIsrael thanks, but i need a formal proof of the theorem, by chance do you have it? – Armando Rosas Dec 12 '17 at 01:01
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See Alan Baker, Transcendental Numbers Theory, theorem 1.4 (Cambridge University Press) – Bernard Dec 12 '17 at 01:10
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At a basic level, Niven, Irrational Numbers. https://books.google.com/books?id=ov-IlIEo47cC&pg=PR7&lpg=PR7&dq=Irrational+Numbers&source=bl&ots=CvtnNVOvUJ&sig=l0o9oKeKJ_u0Fs5ZtfZQwcZedgA&hl=en&sa=X&ved=0ahUKEwjAzMH_rIPYAhUKz2MKHWRODfYQ6AEIaTAN#v=onepage&q=Irrational%20Numbers&f=false – Will Jagy Dec 12 '17 at 01:47
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Analytic Proof Of The Lindemann Theorem – Dec 12 '17 at 04:54