# Tagged Questions

The Laplace transform is a widely used integral transform (transformation of functions by integrals), similar to the Fourier transform.

17 views

### Reason for $0^-$ bound on unilateral Laplace transform

I have the definition of the unilateral $\mathcal{L}$-transform, valid for causal signals, to be: $$\mathcal{L}\left[f(t)\right](s)=\int_{0^-}^{+\infty}f(t)e^{-st}dt$$ My question is regarding the ...
35 views

### Inverse of Mellin transform with lower bound at $1$

I've seen two definitions of the Mellin transform: more commonly, $g$ is the Mellin transform of $f$ if $$g(s)=\int_0^\infty x^{s-1}f(x)\; dx,$$ or secondly, and more rarely, defined by the same ...
36 views

### Why is Laplace transform so useful

I recently encountered the term Laplace transform. Since My background is mathematical, the definition itself is very easy for me. The thing which is less clear for me is the context. I assume, that ...
94 views

### Numerical or analytical or exisistence: Inverse Laplace Transform

Edit 1: With the hint of Ron, we can simplify the question to : $$\bar{f}(s)=\frac{1}{(s^2+1)\arctan s }$$ So what about this function's inverse Laplace Transform? Or can anyone tell me that the ...
148 views

213 views

### Conditions for existence of inverse Laplace transform.

Given a function $F(s)$, how to check if inverse Laplace transform of $F(s)$ exists? In other words, I want to know conditions for existence $f(t)$ such that $$\int_0^\infty e^{-st}f(t)\,ds = F(s)$$...
34 views

31 views

### Inverse Laplace of a function

I am really searching for hours now for the inverse laplace transformation of the following function: $$\frac{75s + 12739.726}{s( 0.0365s^2 + 81.2s + 12739.726)}$$ If I put this in WolframAlpha the ...
270 views

### Laplace transform of inverse gaussian distribution [closed]

Can someone write in details how i can derive the Laplace transform of the Inverse Gaussian distribution? I think i am missing something during the calculation of the interval which gives the Laplace ...
120 views

### What does it mean “Laplace transformable functions”

I am reading about the The convolution operation, and the notion Laplace transformable functions is mentioned there. Doe anyone know what is the definition of Laplace transformable functions? Thank ...
34 views

### Inverse Laplace transform with minus $\Delta$ in denominator

Please help me find this inverse Laplace transform. $$F(s)=\dfrac{2s-3}{s^{2}-2s+2}$$ I couldn't resolve the denominator, because the quadratic has discriminant $\Delta=-4$.
87 views

64 views

267 views

### For Laplace Transforms; What is the interpretation of $s$ compared to $t$? Why is each Laplace transform only defined for some values of $s$?

What is the interpretation of $s$ compared to $t$? Why is each Laplace transform only defined for some values of $s$?
81 views

### use laplace transform to solve the given integral equation

use Laplace transform to solve the given integral equation I don't know how start because it differences on other Laplace question I see before
47 views

69 views

180 views

### Inverse Laplace transform $\mathcal{L}^{-1}\left \{ \ln \left ( 1+\frac{w^{2}}{s^{2}}\right ) \right \}$

Where $s\in \mathbb{C}$. I assume that this would be pretty easily handled by solving it by definition, but I haven't taken courses in complex analysis yet. Also, I can't think of any nice property of ...
195 views

### transforming ordinary generating function into exponential generating function

I have seen a post here that says that you can convert an exponential generating function into an ordinary one with the aid of the Laplace transform. Is it possible to do the reverse transformation? i....
### The Laplace transform of $\exp(t^2)$
A naive attempt to calculate the Laplace transform of the function $f(t)=e^{t^2}$ results in integrals of the form $$\int_0^\infty e^{t^2-st}dt,$$ which obviously don't exist as the integrand grows ...