Uses
G appears in combinatorics, as well as in values of the second polygamma function, also called the trigamma function, at fractional arguments:
Simon Plouffe gives an infinite collection of identities between the trigamma function, π2 and Catalan's constant; these are expressible as paths on a graph.
It also appears in connection with the hyperbolic secant distribution.
Read more about this topic: Catalan's Constant