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 Mar4 comment What is the solution of cos(x)=x? How having closed-form expression is related to being transcedential? Mar4 comment What is the solution of cos(x)=x? more likely a link to Omega constant (fixed point of exponent) and an integral form. Mar4 comment What is the solution of cos(x)=x? Without another function? What do u mean? The answer by giorgiomugnaini gives an analytic solution. Mar4 revised What is the solution of cos(x)=x? fixed formulas Mar4 suggested approved edit on What is the solution of cos(x)=x? Mar4 comment What is the solution of cos(x)=x? What's the point of arguing it is trancedential? Fixed point of the exponent is also transcedential, but can be expressed with an integral, for instance. Mar2 comment Does a non-trivial solution exist for $f'(x)=f(f(x))$? @Julien this answer actually better to be on top, because it addresses exactly the issue of solving the equations of the type you proposed and also gives the exact answer in the closed form to your equation. People who follow the link consisting of your caption likely want to see the result. Mar2 comment Does a non-trivial solution exist for $f'(x)=f(f(x))$? @Julien I expected you to accept my answer because it gives you the exact answer. Mar1 answered Does a non-trivial solution exist for $f'(x)=f(f(x))$? Feb28 revised Closed form solution to $\frac{1}{a-1}= \log a$ added 36 characters in body Feb28 asked Closed form solution to $\frac{1}{a-1}= \log a$ Feb21 comment Why formal power series are not considered a system of hypercomplex numbers? LOL who said you composition of functions should be multiplication? What hypercomplex system is built this way? Feb19 revised Why formal power series are not considered a system of hypercomplex numbers? deleted 12 characters in body Feb5 answered Is there a general formula for solving 4th degree equations? Feb5 comment Are there divergent series that cannot be summed up by any method? @Jack D'Aurizio are u sure it will not be convergent for any methods listed on the wikipedia's page? Feb5 comment Are there divergent series that cannot be summed up by any method? @Jack D'Aurizio so what's the point? Feb5 asked Are there divergent series that cannot be summed up by any method? Feb5 comment Divergent Series The series $\sum_{k=1}^\infty \frac{1}{k}$ can be summed up, for instance using Ramanujan's summation or Cauchy principal value. The sum will be $\gamma$, Euler's constant. Jan24 comment Differentiable only at $x=0$ and $f'(0)>0$ The example of David Mitra satisfies the first two conditions. Jan24 comment Differentiable only at $x=0$ and $f'(0)>0$ @user197137 the definition of derivative is $\lim_{h\to 0}\frac{f(x+h)-f(x)}h$. If it is positive, then there are infinitely many such h that $f(-h) < f(0)< f(h)$