The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Abstract

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

References in corpus (4)

• The q-harmonic oscillator and the Al-Salam and Carlitz polynomials
• The q-harmonic oscillator and an analog of the Charlier polynomials
• A model for the continuous q-ultraspherical polynomials
• An algebraic interpretation of the continuous big q-Hermite polynomials

Cited by in corpus (370)

• A "missing" family of classical orthogonal polynomials
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Fluctuation properties of the TASEP with periodic initial configuration
• Dirac oscillator with nonzero minimal uncertainty in position
• Distance-regular graphs
• Some classical multiple orthogonal polynomials
• Non-commutative Renormalization
• Bohr Hamiltonian with deformation-dependent mass term for the Davidson potential
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Crossing Symmetry in Alpha Space
• A study on the fourth q-Painlevé equation
• Differential equations for generalized Jacobi polynomials
• Orthogonal Polynomials from Hermitian Matrices
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
• CCAP for universal discrete quantum groups
• Bispectrality of multivariable Racah-Wilson polynomials
• An extended class of L2-series solutions of the wave equation
• Commutative association schemes
• The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
• Factorisation of Macdonald polynomials
• Scattering and bound states for a class of non-central potentials
• Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
• Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory
• Properties of some families of hypergeometric orthogonal polynomials in several variables
• Exponential Approximation by Stein's Method and Spectral Graph Theory
• Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
• On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• The ASEP and determinantal point processes
• Finite time corrections in KPZ growth models
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials
• Square ice, alternating sign matrices and classical orthogonal polynomials
• Two-Species Asymmetric Simple Exclusion Process with Open Boundaries
• Exact solution in the Heisenberg picture and annihilation-creation operators
• Modification of Crum's Theorem for `Discrete' Quantum Mechanics
• On triviality of S-matrix in conformal higher spin theory
• Solution of the nonrelativistic wave equation in the tridiagonal representation approach
• Evolution equation for the structure function g_2(x,Q^2)
• Fast Computation of Hahn Polynomials for High Order Moments
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Asymptotics of Plancherel-type random partitions
• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Askey--Wilson polynomials, quadratic harnesses and martingales
• Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
• Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
• Normalized Leonard pairs and Askey-Wilson relations
• Random matrix central limit theorems for nonintersecting random walks
• The structure relation for Askey-Wilson polynomials
• The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar
• Bispectral commuting difference operators for multivariable Askey-Wilson polynomials
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Quantum communication through a spin chain with interaction determined by a Jacobi matrix
• On the order of indeterminate moment problems
• Spherical Functions Associated With the Three Dimensional Sphere
• The integrable multiboson systems and orthogonal polynomials
• Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
• On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parameters
• Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
• Ladder Operators for q-orthogonal Polynomials
• Expansions of one density via polynomials orthogonal with respect to the other
• Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau
• Orthogonal Polynomials from Hermitian Matrices II
• The arctic circle boundary and the Airy process
• The Bivariate Rogers-Szegö Polynomials
• 3nj Morphogenesis and Semiclassical Disentangling
• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
• Askey-Wilson Type Functions, With Bound States
• L2 series solution of the relativistic Dirac-Morse problem for all energies
• Askey-Wilson relations and Leonard pairs
• A multi-dimensional Markov chain and the Meixner ensemble
• Duality of orthogonal polynomials on a finite set
• Big q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))
• q-oscillator from the q-Hermite Polynomial
• The Wigner distribution function for the one-dimensional parabose oscillator
• Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
• Intermediate disorder limits for multi-layer semi-discrete directed polymers
• Degenerate Gauss hypergeometric functions
• The unitary subsector of generalized minimal models
• Laplace Transforms for Integrals of Markov Processes
• The time-dependent Schroedinger equation, Riccati equation and Airy functions
• Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
• Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
• The bi-Poisson process: a quadratic harness
• Casoratian Identities for the Wilson and Askey-Wilson Polynomials
• Extensions of discrete classical orthogonal polynomials beyond the orthogonality
• Zeros of polynomials orthogonal with respect to a signed weight
• The Lerch Zeta Function I. Zeta Integrals
• Quasi Exactly Solvable Difference Equations
• $q$-Classical orthogonal polynomials: A general difference calculus approach
• Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials
• On the partition function of the six-vertex model with domain wall boundary conditions
• Bounds on sets with few distances
• Theta and Riemann xi function representations from harmonic oscillator eigensolutions
• On the Equilibrium Configuration of the BC-type Ruijsenaars-Schneider System
• Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
• Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• The Drinfel'd polynomial of a tridiagonal pair
• Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra
• Shuffling algorithm for boxed plane partitions
• Ultraspherical type generating functions for orthogonal polynomials
• A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
• Classes of Bivariate Orthogonal Polynomials
• Structure of the Three-dimensional Quantum Euclidean Space
• The quantum algebra $U_q(s{l}_2)$ and its equitable presentation
• Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues
• Spectral Analysis of Certain Schrödinger Operators
• Equivalences of the Multi-Indexed Orthogonal Polynomials
• Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
• Dual -1 Hahn polynomials and perfect state transfer
• Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
• Towards data-driven stochastic predictive control
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Limit Profiles for Reversible Markov Chains
• The Wilson function transform
• One Parameter Generalizations of the Fibonacci and Lucas Numbers
• Pfaffian Expressions for Random Matrix Correlation Functions
• Heun operator of Lie type and the modified algebraic Bethe ansatz
• Finite-dimensional irreducible modules for the three-point ${\mathfrak{sl}}_2$ loop algebra
• Properties of the zeros of the polynomials belonging to the Askey scheme
• New Quasi Exactly Solvable Difference Equation
• A bilinear form relating two Leonard systems
• Entanglement of Free Fermions on Johnson Graphs
• Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
• Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process
• Orthogonal Polynomials in Mathematical Physics
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients
• Factorization method for difference equations of hypergeometric type on nonuniform lattices
• On factorization of q-difference equation for continuous q-Hermite polynomials
• Linearization coefficients for orthogonal polynomials using stochastic processes
• Classical versions of q-Gaussian processes: conditional moments and Bell's inequality
• Raising and Lowering Operators for Askey-Wilson Polynomials
• Construction of a Lax Pair for the $E_6^{(1)}$ $q$-Painlevé System
• Quantum Tetrahedra
• An Operator Approach to the Al-Salam-Carlitz Polynomials
• On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures
• Extending the class of solutions of the Dirac equation using tridiagonal matrix representations
• q-Distributions on boxed plane partitions
• Limits of elliptic hypergeometric biorthogonal functions
• Markov processes on partitions
• Multi-Particle Quasi Exactly Solvable Difference Equations
• Transition to sub-Planck structures through the superposition of q-oscillator stationary states
• Towards a classification of the tridiagonal pairs
• A note on generalized $q$-difference equations for general Al-Salam--Carlitz polynomials
• Factorization method for second order functional equations
• sl(2,R) symmetry and solvable multiboson systems
• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• Unified description of q-deformed harmonic oscillators
• On discrete q-ultraspherical polynomials and their duals
• On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
• Generating Functions for Some Families of the Generalized Al-Salam-Carlitz $q$-Polynomials
• Interlaced particle systems and tilings of the Aztec diamond
• Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
• The indeterminate moment problem for the $q$-Meixner polynomials
• From weak coupling to spinning strings
• The semiclassical--Sobolev orthogonal polynomials: a general approach
• sl(2) Operators and Markov Processes on Branching Graphs
• Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
• LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials
• A classification of sharp tridiagonal pairs
• Elliptically Distributed Lozenge Tilings of a Hexagon
• Une $q$-déformation de la transformation de Bargmann polyanalytique
• Two linear transformations each tri-diagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form
• Systems with Intensity Dependent Conversion Integrable by Finite Orthogonal Polynomials
• On a correspondence between quantum SU(2), quantum E(2) and extended quantum SU(1,1)
• On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case
• Approximation Operators, Exponential, q-Exponential, and Free Exponential Families
• WKB and Turning Point Theory for Second Order Difference Equations: External Fields and Strong Asymptotics for Orthogonal Polynomials
• Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
• Finding differential equations for symmetric generalized ultraspherical polynomials by using inversion methods
• A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system
• Mathematical Structure of Relativistic Coulomb Integrals
• A few remarks on quadratic harnesses
• Biorthogonal Expansion of Non-Symmetric Jack Functions
• On Asymptotics of $q$-Gamma Functions
• Limit relations between $q$-Krall type orthogonal polynomials
• Meixner polynomials of the second kind and quantum algebras representing su(1,1)
• Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
• Tridiagonal Symmetries of Models of Nonequilibrium Physics
• Sharp tridiagonal pairs
• The Combinatorics of Al-Salam-Chihara $q$-Laguerre polynomials
• Little q-Legendre polynomials and irrationality of certain Lambert series
• Difference Sturm--Liouville problems in the imaginary direction
• Macdonald-level extension of beta ensembles and large-N limit transition
• Finite-dimensional representations of difference operators, and the identification of remarkable matrices
• Hypergeometric solutions to the q-Painlevé equations
• Harmonic analysis on the SU(2) dynamical quantum group
• Wilson function transforms related to Racah coefficients
• Spectra of observables in the q-oscillator and q-analogue of the Fourier transform
• q-Special functions, an overview
• Enveloping algebra U(gl(3)) and orthogonal polynomials in several discrete indeterminates
• Elliptic Hypergeometric Solutions to Elliptic Difference Equations
• $S{U}_q(3)$ corepresentations and bivariate $q$-Krawtchouk polynomials
• Tridiagonal pairs of Krawtchouk type
• An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
• The structure of a tridiagonal pair
• Elliptic pfaffians and solvable lattice models
• Tridiagonal pairs of $q$-Racah type
• Limit theorems and absorption problems for quantum random walks in one dimension
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Generalized Bochner theorem: characterization of the Askey-Wilson polynomials
• Quantum algebra from generalized q-Hermite polynomials
• After Plancherel formula
• Exactly and quasi-exactly solvable `discrete' quantum mechanics
• Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matrix
• Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A
• Bilinear summation formulas from quantum algebra representations
• Chaotic and Predictable Representations for Multidimensional Lévy Processes
• Generalized coherent states for q-oscillator connected with q-Hermite polynomials
• Generalizations of an integral for Legendre polynomials by Persson and Strang
• The Tetrahedron algebra, the Onsager algebra, and the ${\mathfrak{sl}}_2$ loop algebra
• Meixner polynomials and random partitions
• Wilson Polynomials and the Lorentz Transformation Properties of the Parity Operator
• An integrable (classical and quantum) four-wave mixing Hamiltonian system
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• On the families of polynomials forming a part of the Askey--Wilson scheme and their probabilistic applications
• The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach
• Classical skew orthogonal polynomials in a two-component log-gas with charges $+1$ and $+2$
• Pfaffian Stochastic Dynamics of Strict Partitions
• Arbitrary rank jumps for $A$-hypergeometric systems through Laurent polynomials
• Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graph
• Bidiagonal pairs, the Lie algebra sl_2, and the quantum group U_q(sl_2)
• Non-polynomial extensions of solvable potentials a la Abraham-Moses
• Continuous q-Hermite polynomials: An elementary approach
• Funciones Esféricas Matriciales Asociadas a las Esferas y a los Espacios Proyectivos Reales
• The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel
• Inverse of Infinite Hankel Moment Matrices
• Berezin transform on the quantum unit ball
• Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite
• Dimers and orthogonal polynomials: connections with random matrices
• On the Rational Solutions of q-Painlevé V Equation
• On factorization of $q$-difference equation for continuous $q$-ultraspherical polynomials
• Connection preserving deformations and $q$-semi-classical orthogonal polynomials
• Multiple Meixner-Pollaczek polynomials and the six-vertex model
• A set of orthogonal polynomials, dual to alternative q-Charlier polynomials
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview
• New strings for old Veneziano amplitudes IV.Connections with spin chains and other stochastic systems
• When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
• Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator
• Expectation Values $<r^p>$ for Harmonic Oscillator in $R^n$
• On the shape of a tridiagonal pair
• On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity
• Generalized q-deformed oscillators, q-Hermite polynomials, generalized coherent states
• The Fourier Transform on Quantum Euclidean Space
• Exactly Solvable Quantum Mechanics
• On $q$-analogs of some integrals over GUE
• Quantum $SL(2,\mathbb{R})$ and its irreducible representations
• $\mathbb{C}{P}^{2S}$ sigma models described through hypergeometric orthogonal polynomials
• Five-parameter potential box with inverse square singular boundaries
• $q$-Bessel Functions and Rogers-Ramanujan Type Identities
• Harmonic Analysis on Quantum Complex Hyperbolic Spaces
• Wilson's 6-j laws and stitched Markov processes
• Laguerre and Meixner orthogonal bases in the algebra of symmetric functions
• Transformation design and nonlinear Hamiltonians
• Veneziano Amplitudes, Spin Chains and String Models
• Enveloping superalgebra U(osp(1|2)) and orthogonal polynomials in discrete indeterminate
• q deformation by intertwining with application to the singular oscillator
• On BC type basic hypergeometric orthogonal polynomials
• A generalization of the Mehta-Wang determinant and Askey-Wilson polynomials
• Elliptic polynomials orthogonal on the unit circle with a dense point spectrum
• Fusion and exchange matrices for quantized sl(2) and associated q-special functions
• Orthogonal Basic Hypergeometric Laurent Polynomials
• On Markov processes with polynomials conditional moments
• Factorizacion of the hypergeometric-type difference equation on the uniform lattice
• Squeezed coherent states and the Morse quantum system
• On $q^2$-trigonometric functions and their $q^2$-Fourier transform
• QDYBE: some explicit formulas for exchange matrix and related objects in case of sl(2), q=1
• Difference operators and determinantal point processes
• Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions
• Designs, permutations, and transitive groups
• On the q-convolution on the line
• The switching element for a Leonard pair
• A q-analogue of convolution on the line
• Sums of squares from elliptic pfaffians
• Inversion methods for finding differential equations for generalized Jacobi polynomials
• Laguerre functions and representations of su(1,1)
• Different faces of harmonic oscillator
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Hypergeometric solutions to ultradiscrete Painleve equations
• Tight relative $t$-designs on two shells in hypercubes, and Hahn and Hermite polynomials
• Asymptotics of partition functions in a fermionic matrix model and of related $q$-polynomials
• Coherent States for generalized oscillator with finite-dimensional Hilbert space
• Special functions and the Mellin transforms of Laguerre and Hermite functions
• Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
• Eigenvalues of GUE Minors
• Orthogonal polynomials attached to coherent states for the symmetric Poschl-Teller oscillator
• The Erdős-Ko-Rado basis for a Leonard system
• A discrete weighted Markov--Bernstein inequality for polynomials and sequences
• Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems
• Self-adjoint difference operators and classical solutions to the Stieltjes--Wigert moment problem
• Summation formula for generalized discrete $q$-Hermite II polynomials
• $q$-Racah ensemble and $q$-P$\left(E_7^{(1)}/A_1^{(1)}\right)$ discrete Painlevé equation
• Potential Function Of the Wilson--Racah Quantum System
• New Quantum System of Wilson Orthogonal Polynomial
• Orthogonal polynomials associated with Coulomb wave functions
• Integrable models for quantum media excited by laser radiation: a method, physical interpretation, and examples
• Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator
• Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients
• Even and odd generalized hypergeometric coherent states
• On integration with respect to the q-Brownian motion
• Premixed flame shapes and polynomials
• Towards a q-analogue of the Harer-Zagier formula via rook placements
• Orthogonal Polynomials appearing in SIE grid representations
• New proofs of determinant evaluations related to plane partitions
• The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials
• (q,t)-hook formula for Birds and Banners
• Two non-nilpotent linear transformations that satisfy the cubic $q$-Serre relations
• Quantum communication through Jaynes-Cummings-Hubbard arrays
• Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
• Quantum dimensions and their non-Archimedean degenerations
• Continuous Hahn functions as Clebsch-Gordan coefficients
• Uniform Asymptotics of the Meixner Polynomials
• A new class of Matrix Models arising from the W-infinity Algebra
• Leonard triples and hypercubes
• Bilinear generating functions for orthogonal polynomials
• Fisher information of orthogonal polynomials I
• A second addition formula for continuous q-ultraspherical polynomials
• Hamiltonian Type Operators in Representations of the Quantum Algebra U_q(su_{1,1})
• Enlarging the class of exactly solvable nonrelativistic problems
• The Eigenfunctions of the q-Harmonic Oscillator on the Quantum Line
• A q-analog of the Racah polynomials and the q-algebra SUq(2)
• Asymptotic analysis of the Krawtchouk polynomials by the WKB method
• Electronic transport through a local state linearly coupled to phonon modes
• Orthogonal Polynomials and Generalized Oscillator Algebras
• Construction of Hypergeometric Solutions to the q-Painlevé Equations
• Advanced Determinant Calculus: A Complement
• Correlation functions for random involutions
• Asymptotic distribution of zeros of polynomials satisfying difference equations
• Software for the Algorithmic Work with Orthogonal Polynomials and Special Functions
• Some remarks on a paper by L. Carlitz
• Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
• The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, I
• A factorization method for q-Racah polynomials
• A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
• Askey--Wilson Integral and its Generalizations
• On continuous but differentiable nowhere solutions in the moment problem
• Approximation on the complex sphere
• New isometry of Krall-Laguerre orthogonal polynomials in martingale spaces
• Matrix-Valued Little q-Jacobi Polynomials
• Basic analog of Fourier series on a {\large $\que$}-quadratic grid
• Discrete q-Hermite polynomials: An elementary approach
• Jackson's $(-1)$-Bessel functions with the Askey-Wilson algebra setting
• Eigenvalue density for a class of Jacobi matrices
• Integrals and Series Representations of $q$-Polynomials and Functions: Part II Schur Polynomials and the Rogers-Ramanujan Identities
• Integral representations for a generalized Hermite linear functional
• Efficient modified Jacobi-Bernstein basis transformations
• Meixner $d$-Orthogonal Polynomials Arising from $\mathfrak{su}(1,1)$
• Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials
• The q-Hahn PushTASEP
• Discrete multiple orthogonal polynomials on shifted lattices
• A discrete and $q$ Asymptotic Iteration Method
• Some aspects of positive kernel method of quantization
• The vector-valued big q-Jacobi transform
• A set of $q$-coherent states for the Rogers-Szegő oscillator
• Certain generating functions for Cigler's polynomials
• Self-adjoint difference operators and symmetric Al-Salam--Chihara polynomials
• $q$-difference equation for generalized trivariate $q$-Hahn polynomials
• On a ${\mathbb{C}}^2$-valued integral index transform and bilateral hypergeometric series
• Limits of Random Motzkin paths with KPZ related asymptotics
• Asymptotic analysis of the Hermite polynomials from their differential-difference equation
• Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements
• The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and $U_q(s{l}_2)$
• $q$-Pearson pair and moments in $q$-deformed ensembles
• Semicomplete Arithmetic Sequences, Division of Hypercubes, and the Pell Constant
• Closed-form expressions, generating function and Mehler-Heine type formula for the associated Meixner polynomials and some applications