In the first lecture, I will review the method of steepest descent and its extension by Chester, Friedman and Ursell. Then I will discuss a further extension and its application to some orthogonal polynomials.
View the extended abstract of the first lecture in latex,
In my second lecture, I will present a new interpretation of
Stokes phenomenon due to M.V. Berry and the concept of Exponential Asymptotics.
If time allows, I will also illustrate these new ideas with the generalized
Bessel function and the Mittag-Leffler function.
View the extended abstract of the second lecture in latex, dvi, ps and pdf .