Inverse Laplace transform

  • Thread starter ralqs
  • Start date
  • #1
99
1

Main Question or Discussion Point

According to the Wikipedia page, the inverse Laplace transform is
[tex]f(x) = \frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} F(s')e^{s'x}ds'[/tex]
Something seems wrong though. If I were to take the Laplace transform this equation, I should get F(s) coming out of the right hand side. But when I try this, I get a stray factor of i:
[tex]\mathcal{L}(f(x))=\int_{-\infty}^{\infty}f(x)e^{-sx}dx = \frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} \int_{-\infty}^{\infty} F(s')e^{(s'-s)x}dxds' = \frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} F(s') [\int_{-\infty}^{\infty}e^{(s'-s)x}dx]ds'
\frac{1}{2 \pi i} \lim_{y\rightarrow \infty} \int_{x_0-iy}^{x_0+iy} F(s') \cdot 2 \pi \delta (s'-s)ds'= -i F(s)[/tex]
I would appreciate it if someone could identify my mistake. Thanks.
 

Answers and Replies

  • #2
99
1
Nevermind, I noticed my mistake.
 

Related Threads on Inverse Laplace transform

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
7K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
8
Views
5K
  • Last Post
Replies
2
Views
23K
Replies
2
Views
2K
Top