Romanovski polynomials in selected physics problems

Abstract

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.

RevTex, 38 pages, 2 figures, review

References in corpus (12)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Fredholm Determinants, Differential Equations and Matrix Models
• A new PT symmetric complex Hamiltonian with a real spectra
• The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
• Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance
• Gap probabilities in the finite and scaled Cauchy random matrix ensembles
• On the Parity Degeneracy of Baryons
• Baryons in O(4) and Vibron Model
• Orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics
• Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics
• Orthogonality of Jacobi polynomials with general parameters
• Angular Momentum Dependent Quark Potential of QCD Traits and Dynamical O(4) Symmetry

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• Extending Romanovski polynomials in quantum mechanics
• Conformal symmetry and light flavor baryon spectra
• Exact equivalences and phase discrepancies between random matrix ensembles
• On the exact solubility in momentum space of the trigonometric Rosen-Morse potential
• On polynomial solutions to Fokker-Planck and sinked density evolution equations
• Symmetry and degeneracy of the curved Coulomb potential on the S3 ball
• Exponential generating functions for the associated Bessel functions
• Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity
• Exactness of Bohr-Sommerfeld quantisation for two non-central potentials
• Hua-Pickrell diffusions and differential equations related with pseudo-Jacobi polynomials
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions
• Polyanalytic Reproducing Kernels on the Quantized Annulus