- #1

- 41

- 0

[tex]L[t^n] = \frac{n!}{s^{n+1}}[/tex]

- Thread starter mathwurkz
- Start date

- #1

- 41

- 0

[tex]L[t^n] = \frac{n!}{s^{n+1}}[/tex]

- #2

- 574

- 0

- #3

- 41

- 0

Ah. Ok I got it thanks. I guess I must have let it slip by me that gamma function is related.

- #4

- 2

- 0

You can show that

[tex] \int t^n e^{-ts} dt = -s^{-n-1}\int_{st}^{\infty}x^n e^{-x}dx +c [/tex]

therefore

[tex] \int_{0}^{\infty} t^n e^{-ts} dt =s^{-n-1}\int_{0}^{\infty}x^n e^{-x}dx =s^{-n-1} n![/tex]

- Last Post

- Replies
- 1

- Views
- 2K

- Replies
- 3

- Views
- 4K

- Replies
- 4

- Views
- 2K

- Replies
- 2

- Views
- 784

- Last Post

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 10

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 1K

- Replies
- 3

- Views
- 229