I'm trying to show that if [tex]f(x)[/tex] is analytic, then for large enough n,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|| f^{(n)} (x) || \leq c n! || f(x) ||[/tex],

where

[tex]|| f ||^2=\int_a^b{|f|^2}dx[/tex]

and [tex]f^{(n)}[/tex] denotes the nth derivative.

I tried to use the Taylor series, and then manipulated some inequalities, but I wasn't getting anywhere.

Any ideas?

Thanks

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# Eventual boundedness of nth derivative of an analytic function in L2 norm

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