
Seminar on orthogonal polynomials

主講者:

Prof. Ryu Sasaki (Dept. Physics, NTU)

講題:

New orthogonal polynomials satisfying second order differential equations

時間:

20141204
(Thu.) 12:00  14:00

地點:

數學所 617 研討室 (台大院區)

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) 414417. arXiv:0906.0142[mathph].
``Exactly solvable quantum mechanics and infinite families of multiindexed orthogonal polynomials," Phys. Lett. B702 (2011) 164170. arXiv:1105.0508[mathph].

  Close window 
