Oleg Szehr (Swiss AI Lab IDSIA): New insights on the asymptotic behavior of Jacobi polynomials and applications
Abstract:
Although a recurrent tool in applied asymptotic analysis, the asymptotic behavior of Jacobi polynomials with varying parameters is frequently good for a surprise.
We introduce a new, simple and robust approach to this topic and demonstrate that certain « established » formulas in the literature yield inaccurate results.
Using our method we identify previously unknown forms of asymptotic behavior and we investigate how this affects applications of Jacobi polynomial asymptotics:
1) We show how the Fourier coefficients of powers of Blaschke factors can be written in terms of Jacobi polynomials and we discuss their asymptotic behavior.
2) We discuss the asymptotics of quantum random walks on 1D spin systems using Jacobi polynomials, where we observe a new form of asymptotic behavior.
This talk is based on: https://www.sciencedirect.com/science/article/pii/S0021904522000041