# Tagged Questions

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### $\forall x \,\exists k$ s.t. $f^{(k)}(x)=0$, then $f$ is a polynomial

My friend sent me the following problem: Suppose that $f$ is real analytic on $(a,b)$, and that for all $x$ in $(a,b)$ there exists a non-negative integer $k$ such that $f^{(k)}(x)=0$. Show ...
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### Tthe inverse of a Mellin transform of a polynomial…

Let $\mathcal{M}$ be the symbol of the Mellin transform as define in http://en.wikipedia.org/wiki/Mellin_transform In a calculus, I finally end up with $$\mathcal{M^{-1}(f)}=\mathcal{P}$$ where ...
For $n\in\mathbb{N}$ let $p_n$ be a polynomial of degree $n$. Suppose there exists $c>0$ such that $\bullet$ if $z\in\mathbb{C}$ is a zero of a $p_n$, then $|z^2+c|\leq c$ (note that in particular ...
### Polynomial $p(x) = 0$ for all $x$ implies coefficients of polynomial are zero
I am curious why the following is true. The text I am reading is "An Introduction to Numerical Analysis" by Atkinson, 2nd edition, page 133, line 4. $p(x)$ is a polynomial of the form:  p(x) = ...