The functions G and H turn up in the Rogers–Ramanujan identities, and the function Q is the Euler function, which is closely related to the Dedekind eta function. If x = e, then x G (x), x H (x), x P (x), z, κ, ρ, ρ 1, ρ 2, and ρ 3 are modular functions of τ, while x Q (x) is a modular form of weight 1/2. Since any two modular functions are related by an algebraic relation, this implies that the functions κ, z, R, ρ are all algebraic functions of each other (of quite high degree) (Joyce 1988). In particular, the value of κ (1), which Eric Weisstein dubbed the hard hexagon entropy constant (Weisstein), is an algebraic number of degree 24 equal to 1.395485972... (OEIS : A085851).