On a Biorthogonal System associated with Uniform Asymptotic Expansions

Abstract

In the present paper, a family of rational functions is introduced, and the two families form a biorthogonal system on a contour in the complex plane. The system can be viewed as a generalization of the families {z n } and {z −n−1 }, which occur in Taylor expansions and the Cauchy integrals of analytic functions. Explicit representations of the rational functions are given together with the rigorous estimates