Analytic theory of finite asymptotic expansions in the real domain. Part I: two-term expansions of differentiable functions

摘要

We establish a general analytic theory of asymptotic expansions of type f(x) = a₁ j₁ (x) + ¼+ a_n j_n (x) + o(j_n (x)) x ® x₀ ,f(x) = a_1 varphi _1 (x) + cdots + a_n varphi _n (x) + o(varphi _n (x)) x to x_0 ,