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Top Questions
12
votes
Asymptotics of $\int_0^\infty \frac{x^{2z}}{\Gamma(1+z)}\,dz$ for large $x$
real-analysis
ca.classical-analysis-and-odes
asymptotics
asked Dec 31, 2022 at 6:22
mathoverflow.net
10
votes
Evaluating the integral $\int_0^{\infty} \frac{\sin(x)}{\sinh(x)}\,dx$
calculus
integration
improper-integrals
asked Nov 30, 2017 at 2:24
math.stackexchange.com
8
votes
Is there a real-analytic way to derive the asymptotics of $\int_{-\infty}^\infty e^{ikx} e^{-k^4}\,dk$ as $|x|\to\infty$?
real-analysis
cv.complex-variables
asymptotics
asked Nov 6, 2021 at 2:53
mathoverflow.net
8
votes
How to justify interchange of summation and integral with $f_n(x)=x^2 \cos(2nx)/n$ on $[0, \pi/2]\times \mathbb{N}$?
integration
summation
fourier-analysis
fourier-series
asked Aug 21, 2021 at 21:49
math.stackexchange.com
6
votes
Upper and lower bounds for $\int_0^\infty e^{-u(u^\epsilon -1)}\,du$
real-analysis
inequality
definite-integrals
upper-lower-bounds
asked Mar 8, 2022 at 4:34
math.stackexchange.com
6
votes
Asymptotics of $\int_0^\infty \frac{x^{2z}}{\Gamma(1+z)}\,dz$
integration
definite-integrals
asymptotics
improper-integrals
asked Dec 31, 2022 at 5:57
math.stackexchange.com
5
votes
A conjecture on integrals of infinite products
ca.classical-analysis-and-odes
integration
asked Mar 15, 2020 at 1:18
mathoverflow.net
5
votes
Contour for $\int_0^\infty \arctan(z) e^{-z^2}\,dz$ or some variant
integration
complex-analysis
definite-integrals
contour-integration
complex-integration
asked Dec 28, 2018 at 6:42
math.stackexchange.com
Top Answers
14
Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$
math.stackexchange.com
12
Evaluation of a Fresnel type integral.
math.stackexchange.com
12
Some horrid integrals I am confused with
math.stackexchange.com
12
If $f(x) = \sum_{n=0}^\infty a_n x^n$, then $\int_{-\infty}^\infty f(x^2) dx = \pi i a_{-\frac{1}{2}}$
mathoverflow.net
11
An identity for the elliptic theta function
mathoverflow.net
10
Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.
math.stackexchange.com
8
Motion of a falling object with air resistance
math.stackexchange.com
7
How should I translate "isomorphisme près" to English?
math.stackexchange.com
7
Why doesn't $\sinh(x)$'s Taylor Series divide by half?
math.stackexchange.com
7
Evaluate $\int_{0}^{\infty}2^{-ax^2}dx$ by using Gamma function
math.stackexchange.com
7
Bounding the $n$-th derivatives of $\frac{1-\cos(x)}{x^2}$
mathoverflow.net
6
Why :$\int\frac{dx}{a^2+x^2}= \frac 1a \tan^{-1}(\frac x a )$?
math.stackexchange.com
6
proving convergence of $\int_1^{\infty} \frac{\ln^5(x)}{x^2}dx$
math.stackexchange.com
6
$\int_0^\infty \frac{\sqrt{x}}{x^2+2x+5}\mathrm{d}x$ using Feynman's trick
math.stackexchange.com
6
Using Watson's lemma to derive asymptotic expansion
math.stackexchange.com
5
Sum of $\sum\limits_{k \geq 1} \frac{k^2}{k!}$
math.stackexchange.com
5
What is the closed form solution for this integral or series?
math.stackexchange.com
5
Closed form for $I(b)=\int_0^1\arctan^bx\ \mathrm{d}x$
math.stackexchange.com
5
How to compute $\int_{0}^{\infty}e^{-ax^2}\cos(bx^2)dx$?
math.stackexchange.com
5
best approximation of $\sqrt[3]{8.1}$ using cubic function
math.stackexchange.com
5
Compute the Laplace transform of $\frac{1}{\sqrt{\pi t}} e^{\frac{-a^2}{4t}}$
math.stackexchange.com
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