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Tagged with bell-numbers real-analysis
3
questions
0
votes
2
answers
494
views
Interesting ways to show that there are infinitely many equivalence relations on an infinite set (including Bell numbers).
I am trying to answer the question "Is there infinitely many equivalence relations on any infinite set?"
My intuition says yes, and when I try to prove this, I feel like my reasoning is not ...
- 131
1
vote
1
answer
55
views
Alternative representation for $B_{n,k}(1!,\dots,(n-k+1)!)$
Let $B_{n,k}$ be the Exponential Bell Polynomial and $\hat {B}_{n,k}$ the Ordinary Bell Polynomial. One has the identity:
$$
B_{n,k}(0!,1!,\dots,(n-k)!)
=
|s(n,k)|,
$$
with $s(n,k)$ the Stirling ...
- 1,135
3
votes
1
answer
256
views
What's the sum of the series $\sum\limits_{n\geq 0}\frac{n^x}{n!}$ with $x$ a positive real number?
By the ratio test the series
$$
\sum_{n\ge0}\frac{n^x}{n!}
$$
is convergent, but I know no method to evaluate it.
Since it's a convergent series then my question here is:
Is there a closed form ...
- 7,195