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Results tagged with sequences-and-series
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user 49208
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.
15
votes
Sum of series $a^{i^2}$
This sum equals exactly to:
$$ \frac{1}{2}\left(\theta_3 (0,a) -1 \right),$$
and $\theta_3$ is the Jacobi $\theta$ - function.
- 1,560
5
votes
Is this a rational function?
In Prudnikov, Brychkov, Marichev, vol. 1 there is an explicit formula via basic hypergeometric functions. Not rational.
- 1,560
2
votes
Hypergeometric sum specific value
You may use the general formula from Brychkov, Prudnikov, Marichev, Integral and Series, Vol.3:
$$
_{2}F_{1}(1,1;\frac{1}{2};x)=(1-x)^{-1}\left(1+\frac{\sqrt{x}\arcsin{\sqrt{x}}}{\sqrt{1-x}}\right)
$$ …
- 1,560