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Results tagged with closed-form-expressions
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user 39602
For questions that specifically ask for determining a closed form of equations, integrals etc.
7
votes
1
answer
413
views
Convergence and Closed Form of an Integral Involving Bell Numbers
1. Does the following integral converge ?
$$\int_0^\infty \frac{b(x)}{B(x)} dx$$
where
$$b(x) = \sum_{n=1}^\infty \frac{n^x}{n^n} \qquad and \qquad B(x) = \sum_{n=1}^\infty \frac{n^x}{n!}$$
2. Doe …
- 655
11
votes
1
answer
437
views
Closed Form for $\sum\limits_{n=-2a}^\infty(n+a){2a\choose-n}^4,~a\not\in\mathbb Z$
Do either $~S_4^+(a)~=~\displaystyle\sum_{n=0}^\infty(n+a){2a\choose n}^4~$ or $~S_4^-(a)~=~\displaystyle\sum_{n=-2a}^\infty(n+a){2a\choose-n}^4~$ possess a meaningful closed form expression1 in term …
- 655