I did not know that one! It's a more complex version of the well-known functional definition of the exponential function, i.e. the unique continuous function sa

I did not know that one! It's a more complex version of the well-known functional definition of the exponential function, i.e. the unique continuous function satisfying E(x) E(y) = E(x + y) and a normalization, E(1) = (whatever).