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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
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
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
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
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
Journal Article
2001, ISBN 9781584882107, xxiii, 289
Book
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
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2018, Volume 209, Issue 3, pp. 320 - 351
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2018, Volume 344, pp. 15 - 24
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
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
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 10/2013, Volume 174, Issue 1, pp. 10 - 53
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 2, pp. A629 - A652
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 16
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
Journal Article
1939, 4th ed. --, Colloquium publications - American Mathematical Society, ISBN 0821810235, Volume 23, xiii, 432
Book
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
Journal Article
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