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Tagged with bounds-of-integration improper-integrals
5
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How can I evaluate the bounds of this integral?
I have got this integral from a fourier transform:
$$\int_{-\infty}^0 e^{-ikx+x/4}+\int_0^{\infty} e^{-ikx-x/4}dx$$ Apparently the integrals give:
$$=\frac{1}{1/4 -ik}+\frac{1}{1/4 +ik}$$
But how? I'm ...
- 87
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2
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Upper bound of the integral $\int_\delta^\infty t^m e^{-\nu t^2} dt$
I am reading Wong's book on "Asymptotic Approximations of Integrals". On page 497, the book recalls (without proof) the following estimate: for all $\delta>0$ and $\nu>1$,
$$
\int_\...
- 13.3k
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Limit of ratio of incomplete gamma function
In order to derive Sterling's approximation, I need to show that the following integral decays quicker than at least $\mathcal{O}(n^2)$:
$\lim_{n\to\infty}\dfrac{\int_{2n}^\infty x^ne^{-x}dx}{\int_{0}^...
- 185
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3
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Evaluating $\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$
I am interested in the improper integral: $$I=\int_{-\infty}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x=2\int_{0}^\infty 1-e^{-\frac{1}{x^2}}{\rm d}x$$ which I am fairly sure converges.
I broke the integral ...
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Integrating the bivariate normal distribution [duplicate]
Let $X$ and $Y$ have the bivariate normal density function,
$$ f(x, y) = \frac{1}{2 \pi \sqrt{1 - p^2}} \exp \left\{ - \frac{1}{2(1 - p^2)} (x^2 - 2pxy + y^2) \right\} $$
for fixed $p \in (-1, 1)$. ...
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