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Results tagged with fa.functional-analysis
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user 48831
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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
2
votes
Absolute convergence of logarithm of polynomial with positive coefficient ($\ln G(z) = \sum\...
Not a complete solution, only a remark: assume $G(z)$ has no zeroes in the closed unit disk.
If the series for $G(z)$ has radius of convergence >1 the series for $\log(G(z)$ will converge absolutely i …
- 3,255