Apéry's constant is defined as:
where ζ is the Riemann zeta function.
It has the approximate value 1.202056903...
It also arises in the following way: pick three positive integers at random, then the odds of them having no common divisor are 1 in 1.202056903...
1. Apéry, R. "Irrationalité de ζ(2) et ζ(3)." Astérisque, 61: 11-13 (1979).