- #1

mathwurkz

- 41

- 0

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter mathwurkz
- Start date

- #1

mathwurkz

- 41

- 0

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

- #2

inha

- 576

- 1

- #3

mathwurkz

- 41

- 0

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

- #4

andyL

- 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]

Share:

- Replies
- 22

- Views
- 897

- Last Post

- Replies
- 2

- Views
- 153

- Replies
- 3

- Views
- 574

- Replies
- 14

- Views
- 760

- Replies
- 11

- Views
- 758

- Replies
- 4

- Views
- 470

- Replies
- 1

- Views
- 427

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 9

- Views
- 786

- Last Post

- Replies
- 3

- Views
- 537