scholarly journals Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

2017 ◽  
Vol 522 ◽  
pp. 71-110 ◽  
Author(s):  
P. Baseilhac ◽  
A.M. Gainutdinov ◽  
T.T. Vu
Keyword(s):  
Orthogonal Polynomials ◽  
Higher Order ◽  
Tridiagonal Pairs

scholarly journals HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

2011 ◽  
Vol 26 (25) ◽  
pp. 1843-1852 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Higher Order ◽  
Wave Functions ◽  
Supersymmetric Quantum Mechanics ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials

Exactly solvable rationally-extended radial oscillator potentials, whose wave functions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of kth-order supersymmetric quantum mechanics, with special emphasis on k = 2. It is shown that for μ = 1, 2, and 3, there exist exactly μ distinct potentials of μth type and associated families of exceptional orthogonal polynomials, where μ denotes the degree of the polynomial gμ arising in the denominator of the potentials.

A higher order Sobolev-type inner product for orthogonal polynomials in several variables

2014 ◽  
Vol 68 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Herbert Dueñas ◽  
Luis E. Garza ◽  
Miguel Piñar
Keyword(s):  
Orthogonal Polynomials ◽  
Higher Order ◽  
Inner Product ◽  
Sobolev Type ◽  
Several Variables

Orthogonal polynomials and higher order singular Sturm-Liouville systems

1989 ◽  
Vol 17 (2) ◽  
pp. 99-170 ◽  
Author(s):  
Lance L. Littlejohn ◽  
Allan M. Krall
Keyword(s):  
Orthogonal Polynomials ◽  
Higher Order ◽  
Sturm Liouville
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