Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials

Krall H.L., Frink O., A new class of orthogonal polynomials: the Bessel polynomials,

1949

Earlier work this paper cites.

Inönü E., Wigner E.P., On the contraction of groups and their representations,

1953

Earlier work this paper cites.

Talman J.D., Special functions: a group theoretic approach (based on lectures by Eugene P. Wigner), W.A. Benjamin, Inc., New York – Amsterdam, 1968

1968

Earlier work this paper cites.

Miller Jr. W., Symmetry and separation of variables,

1977

Earlier work this paper cites.

Askey R., An integral of Ramanujan and orthogonal polynomials,

1987

Earlier work this paper cites.

Koornwinder T.H., Group theoretic interpretations of Askey’s scheme of hypergeometric orthogonal polynomials, in Orthogonal Polynomials and their Applications (Segovia, 1986),

1988

Earlier work this paper cites.

Gasper G., Rahman M., Basic hypergeometric series,

1990

Earlier work this paper cites.

Granovskii Y.I., Zhedanov A.S., Lutzenko I.M., Quadratic algebra as a “hidden” symmetry of the Hartmann potential,

1991

Earlier work this paper cites.

Zhedanov A.S., “Hidden symmetry” of Askey–Wilson polynomials,

1991

Earlier work this paper cites.

Granovskii Y.I., Lutzenko I.M., Zhedanov A.S., Mutual integrability, quadratic algebras, and dynamical symmetry,

1992

Earlier work this paper cites.

Granovskii Y.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved space. I. An oscillator,

1992

Earlier work this paper cites.

Granovskii Y.I., Zhedanov A.S., Lutsenko I.M., Quadratic algebras and dynamics in curved space. II. The Kepler problem,

1992

Earlier work this paper cites.

Bonatsos D., Daskaloyannis C., Kokkotas K., Deformed oscillator algebras for two-dimensional quantum superintegrable systems,

1994

Cited alongside, same era.

Létourneau P., Vinet L., Superintegrable systems: polynomial algebras and quasi-exactly solvable Hamiltonians,

1995

Cited alongside, same era.

Izmest’ev A.A., Pogosyan G.S., Sissakian A.N., Winternitz P., Contractions of Lie algebras and separation of variables,

1996

Cited alongside, same era.

Andrews G.E., Askey R., Roy R., Special functions,

1999

Cited alongside, same era.

Kalnins E.G., Miller Jr. W., Pogosyan G.S., Contractions of Lie algebras: applications to special functions and separation of variables,

1999

Cited alongside, same era.

Daskaloyannis C., Ypsilantis K., Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold,

2006

Later among the works it cites.

Daskaloyannis C., Tanoudis Y., Quantum superintegrable systems with quadratic integrals on a two dimensional manifold,

2007

Later among the works it cites.

Kalnins E.G., Kress J.M., Miller Jr. W., Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties,

Original

2007

Later among the works it cites.

Kalnins E.G., Miller Jr. W., Post S., Wilson polynomials and the generic superintegrable system on the 2-sphere,

2007

Later among the works it cites.

Kress J.M., Equivalence of superintegrable systems in two dimensions,

2007

Later among the works it cites.