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Results tagged with sequences-and-series
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user 33672
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
11
votes
3
answers
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Zeros of polynomials related to Jensen polynomial associated with Riemann xi function $\xi(x)$
We encountered polynomials defined by the recursive relations for the coefficients $b_k>0$ as defined below:
$$p_{n}(x)=\sum_{k=0}^{n}\binom{2n}{2k}b_k x^k$$
$$\frac{b_k^2}{b_{k-1}b_{k+1}}=1+\frac{\pi …
- 603
2
votes
1
answer
252
views
a second order difference equation related to a real polynomials which seems to have only re...
I am seeking solutions to the following difference equation:
$$2c_k-c_{k-1}-c_{k+1}=\ln(k+A)-\ln(k+B)$$
where $A>B>0$.
This equation is related to a real polynomial (see here) which I want to prove th …
- 603
1
vote
0
answers
58
views
Bounds on $\sum_{j=1}^m\frac{\pi^j}{\Gamma(j)(x^2+(j+1/4)^2)}$
During our search of real rooted entire function approximations to Riemann $\Xi$ function, we need to calculate the upper and lower bounds of
$$f_m(x):=\sum_{j=1}^m b_j(x):=\sum_{j=1}^m\frac{\pi^j}{\G …
- 603