A Turning Point Theory for Difference Equations

Research Horizons Seminar
Wednesday, September 24, 2008 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 255
Jeff Geronimo – School of Mathematics, Georgia Tech
Ian Palmer
A Turning point is where solutions to differential equations change behavior from exponential to oscillatory. In this region approximate solutions given by the powerful WKB method break down. In a series of paper in the 30's and 40's Langer developed a transformation (the Langer transformation) that allows the development of good approximate solutions (in terms of Airy functions) in the region of the Turning point I will discuss a discrete analog of this transformation and show how it leads to nice asymptotic formulas for various orthogonal polynomials.