asymptotic series

asymptotic series A series formed by the expansion of a function in the form a_o + a₁/x + a₂/x² + … + a_n/xⁿ + …, such that the error resulting from terminating the series at the term a_n/xⁿ tends to zero more rapidly than 1/xⁿ as x tends to infinity. An asymptotic series expansion is not necessarily a convergent series.