Date of Award
Doctor of Philosophy
New results about the strong asymptotic behaviour of diagonal Pade polynomials of high degree are obtained for certain functions with branch points. The method, a modification of a previous approach, uses a singular integral equation for the remainder function restricted to a preferred set. New techniques are developed to analyze three cases (1) a branch point not of square-root type; (2) a case where the preferred set contains three intersecting arcs; (3) a case where not all zeros of the polynomials approach the preferred set.;The first two cases have not previously been treated. The method involves approximating the kernel of the integral equation so that the resulting equation may be solved analytically. The third case has been treated before by a different method, but it is important to show that the new method can handle this case.
Li, Ninghua, "Strong Asymptotics Of Pade Polynomials" (1991). Digitized Theses. 2049.