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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
2
votes
Accepted
finding the limit $\lim_{a\rightarrow \infty} \frac{a^N}{\log a} \int_{0}^\infty \frac{e^{-x...
I propose you take $$g(x):=\frac{N}{c}\exp\frac{-x}{N}.$$ I too doubt that you can find an answer independent on $N$.
The method I used to determine $g$ might lead to an answer which is more intrese …
1
vote
A question about approximation of Real analytic functions
Let me just present the following example which I think relates somehow to the OP question, although it does not answer (anymore) the (now modified) question.
Considering the subset $C$ of power seri …
3
votes
Accepted
How I can choose $(t_1,t_2,...,t_{r}) \in (0,1)^{r}$ such that $f^{(k)}\left(1-2\prod_{j=1}^...
As your question is stated, nothing guarantees that $f^{(k)}$ has a single simple zero. The fact that you introduce extra paremeters cannot change that fact! So, in general, the answer is: there is no …
2
votes
Solving a functional equation
Fact: if you can recover $(f,g)$ from the collection $(h_v)_{v\in V}$ then it must be the unique solution to your problem.
The case $h_v=0$ leads to a lot of non-uniqueness. Otherwise, there is only …
8
votes
Accepted
Is there an algebra for divergent series summation operators?
I'll try to offer as much knowledge as I can on this topic, which might not be that much.
Firstly your linear form $s$ is defined on a strict linear subspace $L$ of the vector spaces of all formal s …
2
votes
Accepted
Analyticity of central stable manifolds
Quick answer to the first question: no, there is no reason why it should be analytic. Take e.g. the parametric vector field (written as a Lie derivative)$$X(x,y):=-x^3\partial_x+(y+\alpha x)\partial_y …