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Results tagged with positivity
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user 4953
16
votes
0
answers
908
views
Polynomials with presumably positive coefficients
After seeing that some positivity problems get their solutions on MO,
I am quite enthusiastic of posing my (and not only) problem of positive flavour. … An additional note in favour of the expected positivity is the limiting case
$n\to\infty$:
$$
P _\infty(q)
=\frac{(q;q) _\infty}{(q^3;q^3) _\infty}
\sum _{r=1}^\infty\frac{q^{r^2}(q^3;q^3) _{r-1}}{(q;q …
- 13.5k
11
votes
0
answers
361
views
Positivity of polynomial sequences via generating series
In this question I address
the problem of proving the nonnegativity of a numerical sequence
$a_0,a_1,a_2,\dots$ via generating series technique. In the notation
$A(x)=\sum_{n=0}^\infty a_nx^n\ge0$ mea …
- 13.5k