Catalan, Euler constant

Moubinool

$\sum_{n\geq0}\frac{(-1)^n}{(2n+1)^2}=G\sim 0.915965...$
$\gamma = \lim_{n\rightarrow \plus \infty}(1+1/2+1/3+...+1/n - ln\;n) \sim 0.577215...$

Are they irrational ?

**Posted:** Sun Oct 17, 2004 12:35 pm

djimenez

Wow! how ignorant one can be... or how missinformed. I had been always told that $\gamma$ was for sure, not only irrational but transcendental. Nevertheless, doing a small research along the web, it seems like both constants are not known to be irrational, those are open problem!!! Does any one wants to give it a try?

**Posted:** Wed Mar 23, 2005 8:10 am

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pat.costello

In the book "Concrete Mathematics" by Graham, Knuth, Patashnik, they say that calculations by Richard Brent have shown that, if Euler's constant is rational, its denominator must be more thatn 10,000 decimal digits long. Therefore nobody believes it is rational, but nobody so far has been able to prove that it is irrational.

**Posted:** Tue Mar 29, 2005 9:08 am