example of four exponentials conjecture
Taking , , , , we see that this conjecture implies that one of , , or is transcendental. Since the first is and the last is , the conjecture states that second must be transcendental, that is, is (conjecturally) transcendental.
In this particular case, the result is known already, so the conjecture is verified. Using Gelfond’s theorem, take and and it follows that is transcendental.
|Title||example of four exponentials conjecture|
|Date of creation||2013-03-22 14:09:09|
|Last modified on||2013-03-22 14:09:09|
|Last modified by||archibal (4430)|