This function is continuous, it follows by M-Weierstrass Test. But proving non-differentiability, I think it's too hard. Does someone know how can I prove this? Or at least have a paper with the proof? The function is $$ f(x) = \sum_{k=1}^\infty \frac{\sin((k + 1)!\;x )}{k!}$$ Thanks!
How to prove that $ f(x) = \sum_{k=1}^\infty \frac{\sin((k + 1)!\;x )}{k!}$ is nowhere differentiable
6
$\begingroup$
calculus
real-analysis
analysis
-
0I wonder if it can be proven using induction and the fundamental theorem of calculus. – 2011-10-31
-
1See also [this question](http://math.stackexchange.com/questions/67120/) -- not an exact duplicate but with much the same properties. – 2011-10-31