Speaker : Prof. Ryu Sasaki (Dept. Physics, NTU)
Title : New orthogonal polynomials satisfying second order differential equations
Time : 2014-12-04 (Thu) 12:00 - 14:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: I present an overview of the newly discovered orthogonal polynomials. They are obtained as the main part of the eigenfunctions of exactly solvable Schroedinger equations. These polynomials start at degree L>=1 and avoiding the constraints of Bochner's theorem but they form a complete basis of orthogonal functions. They are solutions of Fuchsian differential equations with 3+L regular singularities, among which L are ``apparent singularities" located outside of the orthogonality interval. References: S. Odake and R. Sasaki, ``Infinitely many shape invariant potentials and new orthogonal polynomials," Phys. Lett. B679 (2009) 414-417. arXiv:0906.0142[math-ph]. ``Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials," Phys. Lett. B702 (2011) 164-170. arXiv:1105.0508[math-ph].