New posts in laplace-transform

The Laplace transform resolves a function into its moments.

Laplace transform for dummies

$\left[ - \mathcal{L} \left\{ \dfrac{F(t)}{t} \right\} \right]_s^\infty$ to $\mathcal{L} \left\{ \dfrac{F(t)}{t} \right\}\bigg\vert_s$

What is the difference between $e^{it}$ and $e^{st}$

What is the difference between a function and a distribution?

Laplace transform of $ t^{1/2}$ and $ t^{-1/2}$

How is Laplace transform more efficient?

The Laplacian operator is invariant to $SL_2(\mathbb{R})$

Generalized Fresnel integral $\int_0^\infty \sin x^p \, {\rm d}x$

Exponential order in Laplace Transform:constructing a function such that it is of exponential order but its derivative is not.

Laplace transform of $1/t$

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

If $\int_{0}^{\infty} f(x) \, dx $ converges, will $\int_{0}^{\infty}e^{-sx} f(x) \, dx$ always converge uniformly on $[0, \infty)$?

Laplace transform of the Bessel function of the first kind

Connection between the Laplace transform and generating functions

Laplace transform:$\int_0^\infty \frac{\sin^4 x}{x^3} \, dx $

Proof of the unbounded-ness of $\sum_{n\geq 1}\frac{1}{n}\sin\frac{x}{n}$

Convolution Laplace transform

Physical interpretation of Laplace transforms

Inverse Laplace Exponent