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Results tagged with power-series
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user 9833
2
votes
Formal power series is Taylor expansion of rational function iff Hankel determinants vanish?
I am not going to add anything new, just what is my take on it. The proof consists of four really simple steps.
Step I. Determinant is zero iff there exist numbers $b_0,\dots,b_N$, not all of them z …
- 6,891
3
votes
Accepted
Boundary behavior of power series vs. boundedness of partial sums
I think this question is odd because boundedness of $S_N(\xi)$ is a very weak condition whereas existence of an analytic continuation to some open neighborhood of $\xi$ (and even much less nice behav …
- 6,891
4
votes
Comparing two power-series
Here is a proof of the formula
$$\sum_{j>0} \frac{1}{j} w(q)^j P_qw(q)^{-j}=2\log \frac{w(q)}{q}-\log w'(q).$$
(The notation is the same as in the Timothy's answer except I prefer $P_qf(q)$ to $[q^{> …
- 6,891
0
votes
An apparently simple question (behaviour at infinity of a power series)
If there is an uniform convergence, then, for example, $c_n=\sum_{k=0}^n a_kn^k$ will do. But no "reasonable" sequence will work in general, I agree with Loïc Teyssier on this. To say more, one has to …
- 6,891