- #1

- 4

- 0

## Homework Statement

Using Euler's Gamma and a proper substitution prove the relation above:

[itex]\int_0^1 1/x^x=\sum_{n=1}^\infty 1/n^n[/itex]

## Homework Equations

How to resolve this XD?

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 deathquasar
- Start date

- #1

- 4

- 0

Using Euler's Gamma and a proper substitution prove the relation above:

[itex]\int_0^1 1/x^x=\sum_{n=1}^\infty 1/n^n[/itex]

How to resolve this XD?

- #2

- 938

- 9

- #3

- 4

- 0

- #4

- 938

- 9

- #5

- 4

- 0

[itex]\sum_1^\infty \frac{1}{n!}\int_0^\infty e^{-y(n+1)}y^n[/itex]

but now?

- #6

- 938

- 9

Now do a small change of variables so you can write the integral as a gamma function

- #7

- 4

- 0

ok done :D thank you very much ^^

Share: