The real function $cos$ has a unique fixed point. But I have never seen a closed-form expression for that fixed point. I now suspect that there isn't any closed-form expression for that real number. Of course, we first need a definition of closed-form to know if the answer is negative. Has anyone, in some text, rigorously defined closed-form expression and proven that the answer is negative? Or is there in fact a closed-form for that real number?
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7It is not known to have a closed form in any of the usual, preferred ways. You can see some identities by seeing the Wikipedia article on the Dottie number, the name for that fixed point. – PrincessEev Jun 17 '25 at 01:11