Question

Bessel function integral: $\int_{0}^{\infty} e^{-ax}x^{m}\left(J_{0}(bx) \right)^{2} \, \mathrm dx$

score 521 · Answer 1 · 2026-03-28 01:25:51

521

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Bessel function integral: $\int_{0}^{\infty} e^{-ax}x^{m}\left(J_{0}(bx) \right)^{2} \, \mathrm dx$

Published on 28 Mar 2026 - 1:25

score 97 · Answer 2 · 2026-03-28 01:25:49

97

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An improper integral involving Modified Bessel Function of the second kind

Published on 28 Mar 2026 - 1:25

score 385 · Answer 3 · 2019-08-20 11:37:36

385

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Integral $\int^{\infty}_0 \exp\left[-\left(4x+\frac{9}{x}\right)\right] \sqrt{x}\,dx$

Published on 20 Aug 2019 - 11:37

score 25 · Answer 4 · 2019-08-22 14:17:39

25

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$\int_{\mathbf{R}} F^n(ax)f(x)\mathrm{d}x$ with $a>0$ and $f=F^\prime$

Published on 22 Aug 2019 - 14:17

score 62 · Answer 5 · 2019-08-23 18:11:02

62

Views

Is $\lim_{x\to0}x^{p}\int^{x}_1w^{-p}f\left(w\right)dw = 0$?

Published on 23 Aug 2019 - 18:11

score 39 · Answer 6 · 2019-08-23 20:50:31

39

Views

Conditions for convergence of improper integral

Published on 23 Aug 2019 - 20:50

score 509 · Answer 7 · 2019-08-24 04:30:23

509

Views

Rate of decreasing sleeping time question

Published on 24 Aug 2019 - 4:30

score 65 · Answer 8 · 2019-08-24 15:09:57

65

Views

Can the sum property of integrals be stated for indefinite integrals?

Published on 24 Aug 2019 - 15:09

score 787 · Answer 9 · 2019-08-25 08:54:51

787

Views

Why are some improper integrals convergent and others divergent?

Published on 25 Aug 2019 - 8:54

score 262 · Answer 10 · 2026-03-29 02:10:51

262

Views

Improper Fourier transform

Published on 29 Mar 2026 - 2:10

score 73 · Answer 11 · 2026-03-29 03:02:34

73

Views

Can we evaluate this limit? $\lim_{a \rightarrow 0^+}a \int_{b}^{-\log a}\frac{e^y}y \, dy$

Published on 29 Mar 2026 - 3:02

score 380 · Answer 12 · 2026-03-28 03:01:10

380

Views

Evaluate $\int_{-\infty }^{\infty } \left(\cos \left(\sqrt{x^2-1}\right)-\cos \left(\sqrt{x^2+1}\right)\right) \, dx$

Published on 28 Mar 2026 - 3:01

score 124 · Answer 13 · 2019-08-28 16:22:02

124

Views

Show convergence of $\int_1^\infty{\frac{dx}{\sqrt{x^3-x}}}$

Published on 28 Aug 2019 - 16:22

score 203 · Answer 14 · 2019-08-29 01:57:36

203

Views

Approximating $\pi$ and $\ln 2$ with $I_k=\int_0^\infty \left(\text{sech}x\tanh\tfrac12x\right)^k\,dx$ for integer $k$

Published on 29 Aug 2019 - 1:57

score 322 · Answer 15 · 2019-08-29 09:57:37

322

Views

Evaluating the following integral: $\int_{0}^{\infty }\frac{x\cos(ax)}{e^{bx}-1}\ dx$

Published on 29 Aug 2019 - 9:57

List Question

Bessel function integral: $\int_{0}^{\infty} e^{-ax}x^{m}\left(J_{0}(bx) \right)^{2} \, \mathrm dx$

An improper integral involving Modified Bessel Function of the second kind

Integral $\int^{\infty}_0 \exp\left[-\left(4x+\frac{9}{x}\right)\right] \sqrt{x}\,dx$

$\int_{\mathbf{R}} F^n(ax)f(x)\mathrm{d}x$ with $a>0$ and $f=F^\prime$

Is $\lim_{x\to0}x^{p}\int^{x}_1w^{-p}f\left(w\right)dw = 0$?

Conditions for convergence of improper integral

Rate of decreasing sleeping time question

Can the sum property of integrals be stated for indefinite integrals?

Why are some improper integrals convergent and others divergent?

Improper Fourier transform

Can we evaluate this limit? $\lim_{a \rightarrow 0^+}a \int_{b}^{-\log a}\frac{e^y}y \, dy$

Evaluate $\int_{-\infty }^{\infty } \left(\cos \left(\sqrt{x^2-1}\right)-\cos \left(\sqrt{x^2+1}\right)\right) \, dx$

Show convergence of $\int_1^\infty{\frac{dx}{\sqrt{x^3-x}}}$

Approximating $\pi$ and $\ln 2$ with $I_k=\int_0^\infty \left(\text{sech}x\tanh\tfrac12x\right)^k\,dx$ for integer $k$

Evaluating the following integral: $\int_{0}^{\infty }\frac{x\cos(ax)}{e^{bx}-1}\ dx$

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