# Catalan's constant

Catalan's constant is a constant that crops up regularly in combinatorial problems, especially in the evaluation of certain infinite series and integrals. For example, it is equal to

arctan(*x*) / *x* d*x*, and

1 - (1/3)^{2} + (1/5)^{2} - (1/7)^{2} + (1/9)^{2} - ...

It is also the solution to the following problem as *n* becomes arbitrarily
large: If you have a 2*n* × 2*n* checkerboard and a supply
of 2*n*^{2} dominoes that are just large enough to cover
two squares of the checkerboard, how many ways are there to cover the whole
board with the dominoes? Catalan's constant has the value 0.915965...; it
is not known if it is an irrational
number.