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Results tagged with fa.functional-analysis
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user 37436
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
Proof of a Fourier pair with Bessel functions?
The proof is not very complicated, but even a sketch needs more space than a comment. So here is a sketch.
I want to prove that
$$
\int_{-a}^{a} dx \ e^{i y x} \ f(x) = \hat{f}(y)
$$
with $f$ and $\ …
- 1,273
1
vote
Accepted
Limit involving regularized gamma function and its inverse
Below I give a sketch of a proof.
First an approximation for the inverse incomplete gamma function, $Q^{-1}$, is needed.
Henceforth I assume that
$$
g(x)\sim \gamma x^s
$$
for large $x$ with $s>0$. T …
- 1,273
8
votes
Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$
Warning: Nearly every number in this answer is wrong ! Please, read the answer posted by esg, which gives the right asymptotic expansion !
Such problems can be solved by Laplace's method. The startin …
- 1,273
8
votes
Asymptotic expansion of $\sum\limits_{n=1}^{\infty} \frac{x^{2n+1}}{n!{\sqrt{n}} }$
This is another, totally different (and correct !) approach for answering the question. It is simply too long for a comment. So I decided to write it in a new answer. (Although that might look odd, bu …
- 1,273