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Daniele Tampieri
Daniele Tampieri
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soSo i thought about applying the watsonWatson lemma to determine the asymptotic behavior of the integral $\int_{0}^{\infty} \frac{e^{-x(t-ln(t))}}{(1+t^2)} dt$,$$ I(x)=\int_{0}^{\infty} \frac{e^{-x(t-\ln(t))}}{(1+t^2)} dt, $$ as $x \rightarrow \infty$. I think it should be possible to substitute the term $t-ln(t)$$t-\ln(t)$ so that we can apply the lemma. Has anyone an idea on how this could workbe worked out?

so i thought about applying the watson lemma to $\int_{0}^{\infty} \frac{e^{-x(t-ln(t))}}{(1+t^2)} dt$, $x \rightarrow \infty$. I think it should be possible to substitute the term $t-ln(t)$ so that we can apply the lemma. Has anyone an idea on how this could work?

So i thought about applying the Watson lemma to determine the asymptotic behavior of the integral $$ I(x)=\int_{0}^{\infty} \frac{e^{-x(t-\ln(t))}}{(1+t^2)} dt, $$ as $x \rightarrow \infty$. I think it should be possible to substitute the term $t-\ln(t)$ so that we can apply the lemma. Has anyone an idea on how this could be worked out?

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hello
hello
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applying the watson lemma to an integral

so i thought about applying the watson lemma to $\int_{0}^{\infty} \frac{e^{-x(t-ln(t))}}{(1+t^2)} dt$, $x \rightarrow \infty$. I think it should be possible to substitute the term $t-ln(t)$ so that we can apply the lemma. Has anyone an idea on how this could work?