I have been studying Galois theory as of late and recently I came across this proof in the context of Complex Analysis which not only prove the unsolvability of the general quintic and higher degree polynomials using radicals but also using trigonometric and exponential functions.

Is there a proof in the context of Abstract Algebra/ Galois theory that is equivalent? Preferably this proof should follow the same line of reasoning as the Abel-Ruffini theorem (the version that I found on Wikipedia specifically).

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    $\begingroup$ Sorry to be dense, but where exactly is the theorem about trigonometric and exponential functions? I haven’t read through the note in detail, but after a quick scan I can’t find the thing you’re talking about $\endgroup$ Aug 26, 2020 at 8:26
  • $\begingroup$ @qwertiops it is mentioned in the abstract and as the first thing in the section about the insolvability of the quintic. $\endgroup$
    – user208649
    Aug 26, 2020 at 17:30


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