Asymptotic

Asymptotic[expr, x -> x0] gives an asymptotic approximation for expr near x0.

Asymptotic[expr, {x, x0, n}] gives an asymptotic approximation for expr near x0 to order n.

Examples

Asymptotic approximation near infinity:

Asymptotic[Sqrt[1 + 1/x], x -> Infinity]
(* 1 + 1/(2 x) *)

With specified order:

Asymptotic[Gamma[x], {x, Infinity, 2}]

Please visit the official Wolfram Language Reference for more details.