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.