01/2019, ISBN 9783039216215

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics....

eBook

Journal of Approximation Theory, ISSN 0021-9045, 03/2019, Volume 239, pp. 72 - 112

In this paper we present a systematic way to describe exceptional Jacobi polynomials via two partitions. We give the construction of these polynomials and...

Jacobi polynomials | Partitions | Wronskian | Exceptional polynomials | MATHEMATICS | ORTHOGONAL POLYNOMIALS | ZEROS | Mathematics - Classical Analysis and ODEs

Jacobi polynomials | Partitions | Wronskian | Exceptional polynomials | MATHEMATICS | ORTHOGONAL POLYNOMIALS | ZEROS | Mathematics - Classical Analysis and ODEs

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2019, Volume 49, Issue 3, pp. 209 - 228

We show that the flagged Grothendieck polynomials defined as generating functions of flagged set-valued tableaux of Knutson et al. (J Reine Angew Math...

vexillary permutations | 14M15 | Grothendieck polynomials | Mathematics | 13D15 | Convex and Discrete Geometry | Jacobi–Trudi formula | 05E05 | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | flagged set-valued tableaux | MATHEMATICS | Jacobi-Trudi formula

vexillary permutations | 14M15 | Grothendieck polynomials | Mathematics | 13D15 | Convex and Discrete Geometry | Jacobi–Trudi formula | 05E05 | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | flagged set-valued tableaux | MATHEMATICS | Jacobi-Trudi formula

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2017, Volume 296, pp. 1 - 17

•Operational matrix of shifted Jacobi polynomials is considered.•Solution of time-fractional order convection–diffusion problem is numerically estimated.•Main...

Jacobi polynomials | Time-fractional convection–diffusion equation | Caputo fractional derivative | OPERATIONAL MATRIX | MATHEMATICS, APPLIED | Time-fractional convection-diffusion equation | DIFFERENTIAL-EQUATIONS | TERM | HOMOTOPY ANALYSIS METHOD | Differential equations

Jacobi polynomials | Time-fractional convection–diffusion equation | Caputo fractional derivative | OPERATIONAL MATRIX | MATHEMATICS, APPLIED | Time-fractional convection-diffusion equation | DIFFERENTIAL-EQUATIONS | TERM | HOMOTOPY ANALYSIS METHOD | Differential equations

Journal Article

Constructive Approximation, ISSN 0176-4276, 2019, Volume 51, Issue 2, pp. 353 - 381

We investigate type I multiple orthogonal polynomials on r intervals that have a common point at the origin and endpoints at the r roots of unity omega j,...

Jacobi–Angelesco polynomials | Differential equation | Recurrence relation | Asymptotic zero distribution | Multiple orthogonal polynomials | MATHEMATICS | Jacobi-Angelesco polynomials | Mathematics - Classical Analysis and ODEs

Jacobi–Angelesco polynomials | Differential equation | Recurrence relation | Asymptotic zero distribution | Multiple orthogonal polynomials | MATHEMATICS | Jacobi-Angelesco polynomials | Mathematics - Classical Analysis and ODEs

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 02/2020, Volume 250, p. 105324

We investigate the type I and type II multiple orthogonal polynomials on an r-star with weight function |x|βe−xr, with β>−1. Each measure μj, for 1≤j≤r, is...

Jacobi–Angelesco polynomials | Laguerre–Angelesco polynomials | Recurrence relation | Differential equation | Asymptotic zero distribution | Multiple orthogonal polynomials | SYSTEM | MATHEMATICS | PADE APPROXIMANTS | Laguerre-Angelesco polynomials | Jacobi-Angelesco polynomials | Mathematics - Classical Analysis and ODEs

Jacobi–Angelesco polynomials | Laguerre–Angelesco polynomials | Recurrence relation | Differential equation | Asymptotic zero distribution | Multiple orthogonal polynomials | SYSTEM | MATHEMATICS | PADE APPROXIMANTS | Laguerre-Angelesco polynomials | Jacobi-Angelesco polynomials | Mathematics - Classical Analysis and ODEs

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 8/2015, Volume 81, Issue 3, pp. 1023 - 1052

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in...

Jacobi polynomials | Modified generalized Laguerre polynomials | Tau method | Bernstein polynomials | Engineering | Vibration, Dynamical Systems, Control | Generalized Laguerre polynomials | Multi-term FDEs | Mechanics | Automotive Engineering | Mechanical Engineering | Operational matrices | Legendre polynomials | Collocation method | Chebyshev polynomials | EXISTENCE | NONLINEAR SINE-GORDON | DIFFERENTIAL-EQUATIONS | DIFFUSION EQUATION | ENGINEERING, MECHANICAL | ORDER | NUMERICAL-SOLUTION | MECHANICS | INTEGRATION | SYSTEMS | COLLOCATION APPROXIMATION | WAVELETS METHOD | Electrical engineering | Domains | Intervals | Integrals | Differential equations | Chebyshev approximation | Spectra | Polynomials | Derivatives | Matrix methods | Fractional calculus

Jacobi polynomials | Modified generalized Laguerre polynomials | Tau method | Bernstein polynomials | Engineering | Vibration, Dynamical Systems, Control | Generalized Laguerre polynomials | Multi-term FDEs | Mechanics | Automotive Engineering | Mechanical Engineering | Operational matrices | Legendre polynomials | Collocation method | Chebyshev polynomials | EXISTENCE | NONLINEAR SINE-GORDON | DIFFERENTIAL-EQUATIONS | DIFFUSION EQUATION | ENGINEERING, MECHANICAL | ORDER | NUMERICAL-SOLUTION | MECHANICS | INTEGRATION | SYSTEMS | COLLOCATION APPROXIMATION | WAVELETS METHOD | Electrical engineering | Domains | Intervals | Integrals | Differential equations | Chebyshev approximation | Spectra | Polynomials | Derivatives | Matrix methods | Fractional calculus

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 6, pp. 2046 - 2060

The Galerkin method offers a powerful tool in the solution of differential equations and function approximation on the real interval [−1, 1]. By expanding the...

Jacobi polynomials | Spectral method | Gram-Schmidt | Polar coordinates | Sobolev norm | Orthogonality | Galerkin | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | 2ND-ORDER | PHYSICS, MATHEMATICAL

Jacobi polynomials | Spectral method | Gram-Schmidt | Polar coordinates | Sobolev norm | Orthogonality | Galerkin | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | 2ND-ORDER | PHYSICS, MATHEMATICAL

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2018, Volume 209, Issue 3, pp. 320 - 351

We present a conjecture that the asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable...

Abel-Jacobi inversion | complex Greens and Martin functions | reproducing kernel | hyperelliptic Riemann surface | Chebyshev polynomial | analytic capacity | INTERPOLATION | SYSTEM | MATHEMATICS | complex Green's and Martin functions | THEOREM | hyperelliptic Rie-mann surface | CHEBYSHEV POLYNOMIALS | Domains | Entire functions | Analytic functions | Asymptotic properties | Mathematical analysis | Chebyshev approximation | Hilbert space | Polynomials | Continuity (mathematics)

Abel-Jacobi inversion | complex Greens and Martin functions | reproducing kernel | hyperelliptic Riemann surface | Chebyshev polynomial | analytic capacity | INTERPOLATION | SYSTEM | MATHEMATICS | complex Green's and Martin functions | THEOREM | hyperelliptic Rie-mann surface | CHEBYSHEV POLYNOMIALS | Domains | Entire functions | Analytic functions | Asymptotic properties | Mathematical analysis | Chebyshev approximation | Hilbert space | Polynomials | Continuity (mathematics)

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2018, Volume 344, pp. 15 - 24

This paper presents a computational technique based on a special family of the Müntz–Legendre polynomials to solve a class of Volterra–Fredholm integral...

Jacobi polynomials | Volterra–Fredholm integral equations | Müntz–Legendre polynomials | Chebyshev–Gauss–Lobatto points | Least squares approximation method | Convergence analysis | MATHEMATICS, APPLIED | APPROXIMATION | Volterra-Fredholm integral equations | Muntz-Legendre polynomials | Chebyshev-Gauss-Lobatto points | DIFFERENTIAL-EQUATIONS | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | 2ND KIND

Jacobi polynomials | Volterra–Fredholm integral equations | Müntz–Legendre polynomials | Chebyshev–Gauss–Lobatto points | Least squares approximation method | Convergence analysis | MATHEMATICS, APPLIED | APPROXIMATION | Volterra-Fredholm integral equations | Muntz-Legendre polynomials | Chebyshev-Gauss-Lobatto points | DIFFERENTIAL-EQUATIONS | SYSTEMS | INTEGRODIFFERENTIAL EQUATIONS | 2ND KIND

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 537 - 543

New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and...

Bernstein basis polynomials | Dual Bernstein polynomials | Jacobi and Hahn polynomials | Recurrence relations | Generalized hypergeometric functions | Differential equations | BEZIER CURVES | MATHEMATICS, APPLIED | DEGREE REDUCTION

Bernstein basis polynomials | Dual Bernstein polynomials | Jacobi and Hahn polynomials | Recurrence relations | Generalized hypergeometric functions | Differential equations | BEZIER CURVES | MATHEMATICS, APPLIED | DEGREE REDUCTION

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2019, Volume 88, Issue 319, pp. 2351 - 2381

We present a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence \{P_k(x)\}_{k \geqslant 0}...

Jacobi polynomials | MATHEMATICS, APPLIED | Gegenbauer polynomials | Convolution | Laguerre polynomials | REPRESENTATIONS | Volterra convolution integral | CONNECTION COEFFICIENTS | Legendre polynomials | Chebyshev polynomials | orthogonal polynomials

Jacobi polynomials | MATHEMATICS, APPLIED | Gegenbauer polynomials | Convolution | Laguerre polynomials | REPRESENTATIONS | Volterra convolution integral | CONNECTION COEFFICIENTS | Legendre polynomials | Chebyshev polynomials | orthogonal polynomials

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 10/2013, Volume 174, Issue 1, pp. 10 - 53

We introduce the concept of D-operators associated to a sequence of polynomials (pn)n and an algebra A of operators acting in the linear space of polynomials....

Jacobi polynomials | Differential and difference operators | Laguerre polynomials | Classical discrete orthogonal polynomials | Meixner polynomials | Krawtchouk polynomials | Classical orthogonal polynomials | Krall polynomials | Hahn polynomials | Charlier polynomials | COMMUTATIVE ALGEBRAS | CLASSIFICATION | MATHEMATICS | LAGUERRE-POLYNOMIALS | Algebra | Differential equations

Jacobi polynomials | Differential and difference operators | Laguerre polynomials | Classical discrete orthogonal polynomials | Meixner polynomials | Krawtchouk polynomials | Classical orthogonal polynomials | Krall polynomials | Hahn polynomials | Charlier polynomials | COMMUTATIVE ALGEBRAS | CLASSIFICATION | MATHEMATICS | LAGUERRE-POLYNOMIALS | Algebra | Differential equations

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 2, pp. A629 - A652

A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control problems for...

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

High-dimensional approximation | Nonlinear dynamics | Hamilton–Jacobi–Bellman equations | Polynomial approximation | Optimal feedback control | MATHEMATICS, APPLIED | polynomial approximation | high-dimensional approximation | STABILIZATION | optimal feedback control | Hamilton-Jacobi-Bellman equations | nonlinear dynamics

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 16

As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the...

Laguere polynomials | exceptional orthogonal polynomials | discrete QM with real shifts | Jacobi | little q-Jacobi(Laguerre) polynomials | Meixner | exactly solvable QM | multi-indexed orthogonal polynomials | PHYSICS, MULTIDISCIPLINARY | POTENTIALS | PHYSICS, MATHEMATICAL | FAMILIES | HIGHER-ORDER DIFFERENCE | ORTHOGONAL POLYNOMIALS | QUANTUM-MECHANICS | OPERATORS

Laguere polynomials | exceptional orthogonal polynomials | discrete QM with real shifts | Jacobi | little q-Jacobi(Laguerre) polynomials | Meixner | exactly solvable QM | multi-indexed orthogonal polynomials | PHYSICS, MULTIDISCIPLINARY | POTENTIALS | PHYSICS, MATHEMATICAL | FAMILIES | HIGHER-ORDER DIFFERENCE | ORTHOGONAL POLYNOMIALS | QUANTUM-MECHANICS | OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 2, pp. 1082 - 1100

We prove a general expansion formula in Askey–Wilson polynomials using Bailey transform and Bressoud inversion. As applications, we give new proofs and...

Bressoud inversion | Andrews formula | Nassrallah–Rahman integral | Bailey transform | Expansion formulae | Askey–Wilson polynomials | MATHEMATICS, APPLIED | Nassrallah-Rahman integral | SERIES | IDENTITIES | SUMMATION | Askey-Wilson polynomials | INTEGRALS | MATHEMATICS | Q-JACOBI | Mathematics | General Mathematics | Classical Analysis and ODEs

Bressoud inversion | Andrews formula | Nassrallah–Rahman integral | Bailey transform | Expansion formulae | Askey–Wilson polynomials | MATHEMATICS, APPLIED | Nassrallah-Rahman integral | SERIES | IDENTITIES | SUMMATION | Askey-Wilson polynomials | INTEGRALS | MATHEMATICS | Q-JACOBI | Mathematics | General Mathematics | Classical Analysis and ODEs

Journal Article

1939, 4th ed. --, Colloquium publications - American Mathematical Society, ISBN 0821810235, Volume 23, xiii, 432

Book

Pramana, ISSN 0304-4289, 8/2019, Volume 93, Issue 2, pp. 1 - 14

A method to construct the multi-indexed exceptional Laguerre polynomials using the isospectral deformation technique and quantum Hamilton–Jacobi (QHJ)...

rational potentials | Astrophysics and Astroparticles | exactly solvable models | quantum Hamilton–Jacobi formalism | Physics, general | shape invariance | Physics | Astronomy, Observations and Techniques | Exceptional orthogonal polynomials | isospectral deformation | 03.65.Ge | 03.65.Sq | 02.30.Hq | quantum Hamilton-Jacobi formalism | PHYSICS, MULTIDISCIPLINARY | SOLVABLE POTENTIALS | FAMILIES | SHAPE INVARIANT POTENTIALS | SUSY

rational potentials | Astrophysics and Astroparticles | exactly solvable models | quantum Hamilton–Jacobi formalism | Physics, general | shape invariance | Physics | Astronomy, Observations and Techniques | Exceptional orthogonal polynomials | isospectral deformation | 03.65.Ge | 03.65.Sq | 02.30.Hq | quantum Hamilton-Jacobi formalism | PHYSICS, MULTIDISCIPLINARY | SOLVABLE POTENTIALS | FAMILIES | SHAPE INVARIANT POTENTIALS | SUSY

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2005, Volume 178, Issue 1, pp. 215 - 234

A suite of Matlab programs has been developed as part of the book “Orthogonal Polynomials: Computation and Approximation” Oxford University Press, Oxford,...

Recurrence relations | Orthogonal polynomials | Matlab | QUADRATURE-FORMULAS | MATHEMATICS, APPLIED | recurrence relations | JACOBI MATRICES | orthogonal polynomials

Recurrence relations | Orthogonal polynomials | Matlab | QUADRATURE-FORMULAS | MATHEMATICS, APPLIED | recurrence relations | JACOBI MATRICES | orthogonal polynomials

Journal Article

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