Catalan's constant

Catalan's constant K, which occasionally appears in estimates in combinatorics, is defined by

<math>K = \frac{1}{1^2} - \frac{1}{3^2} + \frac{1}{5^2} - \frac{1}{7^2} + ...<math>

or equivalently

<math>K = -\int_{0}^{1} \frac{\ln(t)}{1 + t^2} \mbox{ d} t<math>

Its numerical value is approximately

K = .915 965 594 177 219 015 054 603 514 932 384 110 774 ...

It is not known whether K is rational or irrational.