- #1

- 41

- 0

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

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- Thread starter mathwurkz
- Start date

- #1

- 41

- 0

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

- #2

- 575

- 1

- #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]

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