adj. 1. (of a function, series, etc.) approaching a given value (its asymptote) arbitrarily closely, as the independent variable, or some expression containing a variable, approaches a limit or tends to infinity. Graphically, the perpendicular distance between a curve and its asymptote tends to zero as the distance from the origin tends to a limit or infinity; in this limit is zero. 2. (of a pair of functions) approaching one another infinitely closely as their arguments tend to infinity or some other value; this is often written as f(x) ~ g(x), when For example, as shown below,
sin x ~ x cos x
as x tends to zero, and
2cosh x ~ exp x
as x tends to infinity. See order notation. See also prime number theorem.