# Novel constant

1. Dec 28, 2008

### Loren Booda

$$\sum _{s =1}^{\infty}s^{-s}= ?$$

$$\int _{1}^{\infty}s^{-s}ds= ?$$

Does either this summation or integral define a fundamental constant?

2. Dec 29, 2008

### CRGreathouse

The sum is 1.291285997062663540407282590595600541498619368274..., Sloane's A073009.

The integral is 1.99545595750013800041872469845272435208621663... Both sum and integral are easy to calculate to a large number of decimal places.

The integral over 0 to 1 has the same value as the sum. I wasn't able to find anything interesting about the integral from 1 to infinity.

3. Dec 29, 2008

### Loren Booda

Thank you for your research, CR. I guess they have no direct derivation from the constant e.