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Results tagged with recurrences
Search options questions only
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user 2807
8
votes
1
answer
233
views
A recurrence satisfied by a function asymptotic to $n^n$
A function $f\colon \{0,1,\dots\}\to \mathbb{R}$ is P-recursive if
it satisfies a recurrence
$$ P_d(n)f(n+d)+P_{d-1}(n)f(n+d-1)+\cdots+P_0(n)f(n)=0,\ n\geq 0, $$
where each $P_i(n)\in \mathbb{R}[n]$ a …
- 50.8k
21
votes
5
answers
2k
views
A question on the Laurent phenomenon
I am wondering
whether the same technique might apply to other Laurent phenomenon
recurrences, or whether it can be proved in certain cases that such an
approach cannot work. …
- 50.8k
14
votes
0
answers
273
views
A conjectured rational generating function
In regard to my question here, let $G_n$
be a sequence of positive integers satisfying
$\lim_{n\to\infty}G_n=\infty$, such that the generating function
$\sum_{n\geq 1} G_nx^n$ is rational. Let
$$ P_n( …
- 50.8k
8
votes
0
answers
148
views
Can P-recursive functions assume only prime values?
What about more general recurrences? For instance, let
$F(x)=\sum f(n)x^n\in\mathbb{Z}[[x]]$, where $f(n)$ is
unbounded. …
- 50.8k