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Results tagged with asymptotics
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user 545190
Asymptotic behavior of functions, asymptotic series and related topics
0
votes
2
answers
127
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Asymptotic behavior of the integral of Hermite functions/polynomials on half-lines
I would like to understand the asymptotic behaviour of the following integrals with fixed $x_0>0$:
$$J_m=\int^{+\infty}_{x_0}|H_m(x)|^2 e^{-x^2}dx,$$
where $H_m(x)$ is the $m-$th Hermite polynomial. F …
- 21
1
vote
0
answers
17
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Asymptotic behavior of the Hermite functions
I would like to understand the asymptotic behavior of the Hermite function :
$$\psi_k(x) = \frac{1}{\sqrt{2^k k!}}H_k(x) e^{-\frac{x^2}{2}},$$
where $H_k(x)$ is the $k-$th Hermite polynomial. For inst …
- 21