Question

A customer queue where service time is exponentially distributed and arrival governed by a Poisson process.

score 343 · Answer 1 · 2026-04-13 07:49:11

343

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A customer queue where service time is exponentially distributed and arrival governed by a Poisson process.

Published on 13 Apr 2026 - 7:49

score 381 · Answer 2 · 2026-04-14 03:22:19

381

Views

Definition of heavy tails and moment generating functions

Published on 14 Apr 2026 - 3:22

score 193 · Answer 3 · 2026-04-17 03:37:49

193

Views

Compute the Laplace transform of $\frac{1}{\sqrt{\pi t}} e^{\frac{-a^2}{4t}}$

Published on 17 Apr 2026 - 3:37

score 172 · Answer 4 · 2026-04-14 06:34:36

Inverse Laplace transform of $\frac{a\sinh\left[\frac{p}{c}(L-x)\right]}{p\sinh\left[\frac{pL}{c}\right]}$ with respect to $p$ using binomial theorem

score 2.6k · Answer 5 · 2026-04-16 18:44:04

2.6k

Views

Compute Laplace transform of a triangle wave

Published on 16 Apr 2026 - 18:44

score 1.3k · Answer 6 · 2026-04-16 04:55:11

1.3k

Views

Proving the Laplace transform of $t^n e^{at}$ using mathematical induction

Published on 16 Apr 2026 - 4:55

score 72 · Answer 7 · 2026-04-17 09:05:05

72

Views

Generalize $ \int_0^\infty \frac{t^3 \, dt}{e^t + 1} = \frac{7 \cdot 31}{8} \zeta(4)$ to the number field $\mathbb{Q}(i)$

Published on 17 Apr 2026 - 9:05

score 87 · Answer 8 · 2026-04-15 03:30:01

87

Views

Given that $\int_0^\infty e^{-at}f(t)dt=\frac{1}{\sqrt{a^2+1}}$, what is $\int_0^{\infty}f(t)dt?$

Published on 15 Apr 2026 - 3:30

score 208 · Answer 9 · 2026-04-14 10:32:12

208

Views

How to prove that if $g*g=0$, then $g=0$?

Published on 14 Apr 2026 - 10:32

score 69 · Answer 10 · 2026-04-11 18:20:12

69

Views

LOTUS for Laplace Space

Published on 11 Apr 2026 - 18:20

score 81 · Answer 11 · 2026-04-15 20:54:51

81

Views

Show that the Laplace transform of a $C^1$ function f equal to its derivative at 0.

Published on 15 Apr 2026 - 20:54

score 86 · Answer 12 · 2026-04-12 18:07:11

86

Views

Laplace transform on a continuous function on [0,1]

Published on 12 Apr 2026 - 18:07

score 114 · Answer 13 · 2026-04-16 19:03:51

114

Views

Showing $\int_0^\infty x^2e^{-\mu x^2}\ln x\, \mathrm dx=\frac{1}{8\mu}(2-\ln 4\mu-C)\sqrt{\frac{\pi}{\mu}}$

Published on 16 Apr 2026 - 19:03

score 206 · Answer 14 · 2026-04-15 22:46:12

206

Views

Proving $\mathcal{L}^{-1}(0) =0$ by definition of the Laplace transform.

Published on 15 Apr 2026 - 22:46

score 247 · Answer 15 · 2026-04-13 15:00:03

247

Views

Laplace transform of $e^{-at}$: Using analytic continuation to get a bigger ROC

Published on 13 Apr 2026 - 15:00

List Question

A customer queue where service time is exponentially distributed and arrival governed by a Poisson process.

Definition of heavy tails and moment generating functions

Compute the Laplace transform of $\frac{1}{\sqrt{\pi t}} e^{\frac{-a^2}{4t}}$

Inverse Laplace transform of $\frac{a\sinh\left[\frac{p}{c}(L-x)\right]}{p\sinh\left[\frac{pL}{c}\right]}$ with respect to $p$ using binomial theorem

Compute Laplace transform of a triangle wave

Proving the Laplace transform of $t^n e^{at}$ using mathematical induction

Generalize $ \int_0^\infty \frac{t^3 \, dt}{e^t + 1} = \frac{7 \cdot 31}{8} \zeta(4)$ to the number field $\mathbb{Q}(i)$

Given that $\int_0^\infty e^{-at}f(t)dt=\frac{1}{\sqrt{a^2+1}}$, what is $\int_0^{\infty}f(t)dt?$

How to prove that if $g*g=0$, then $g=0$?

LOTUS for Laplace Space

Show that the Laplace transform of a $C^1$ function f equal to its derivative at 0.

Laplace transform on a continuous function on [0,1]

Showing $\int_0^\infty x^2e^{-\mu x^2}\ln x\, \mathrm dx=\frac{1}{8\mu}(2-\ln 4\mu-C)\sqrt{\frac{\pi}{\mu}}$

Proving $\mathcal{L}^{-1}(0) =0$ by definition of the Laplace transform.

Laplace transform of $e^{-at}$: Using analytic continuation to get a bigger ROC

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