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Results tagged with sequences-and-series
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user 48831
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
What's the summation of formal series $\sum_{n\geq0}\binom{n\delta}{n}x^n$？
The Bürmann-Lagrange theorem gives that
$$\sum_{n\geq 0} {n\delta \choose n} t^n = \frac{1}{1-\delta t(1+z)^{\delta -1}}=\frac{1+z}{1+(1-\delta) z}$$
where $z=z(t)=\sum_{n\geq 1} \frac{1}{n}{n\delta \ …
- 20.2k
21
votes
Accepted
Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$
I sketch the arguments for $C(x)$, the arguments for $L(x)$ are essentially the same.
The specific form of the sum suggests probabilistic arguments.
Let $X_x$ be a $\mathrm{Poiss}(x^2)$-distributed …
- 3,255