Jenny's Constant

Jenny's constant is the name given (Munroe 2012) to the positive real constant defined by

(1) (2)

(OEIS A182369), the first few digits of which are 867-5309, corresponding to the fictitious phone number in the song "867-5309/Jenny" performed by Tommy Tutone in 1982.

Other "simple" expressions that might vie for that moniker include

(3) (4) (5) (6) (7) (8) (9) (10)

where is the hard hexagon entropy constant, the first three of which are "better" than the canonical Jenny expression (E. Weisstein, Jul. 12, 2013).