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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
1
vote
1
answer
118
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Asymptotics of the integral of an oscillating function
I would like to know the asymptotics of the following sequences of integrals:
$$ I_n = \displaystyle { \int _0 ^{+ \infty}
\dfrac{t^n}{(t + i)^{n + 1}}
…
1
vote
Asymptotics of a sequences of integrals
Let us assume the following conjecture:
Let $h: \mathbb{R}^+ \longrightarrow \mathbb{R}$ be a continuous function.
Let also $g_n: \mathbb{R}^+ \longrightarrow \mathbb{R}$ be a $\mathcal{C}^2$ functio …
3
votes
2
answers
134
views
Asymptotics of a sequences of integrals
I would like to know the asymptotics of the following sequences of integrals:
$$ I_n = \int _0
^{+ \infty}
e^{-t} \left ( \dfrac{t}{1 + t} \right )^n
…