Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)

The Guest Editors for this special issue are

Peter Clarkson (University of Kent at Canterbury, UK)
Erik Koelink (Radboud University Nijmegen, The Netherlands)
Ana Loureiro (University of Kent at Canterbury, UK)
Walter Van Assche (University of Leuven, Belgium)

The issue is related to the 14th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA14), held at the University of Kent, Canterbury, UK, July 3–7, 2017. Conferences in the OPSFA series provide a forum for mathematicians, physicists, computational scientists, and application scientists in other fields to communicate recent research results in the areas of orthogonal polynomials and special functions (OPSF). Some 156 participants took a pelgrimage to the city of Canterbury to tell a tale or to listen to one of the many interesting tales by the plenary lecturers and the contributed speakers. The organizers have succeeded to set up a diverse collection of plenary talks, both in scope and gender, reflecting recent activity in our field. Orthogonal polynomials were still prominent, with Chebyshev polynomials, exceptional orthogonal polynomials, Jacobi matrices, multivariate orthogonal polynomials and cubature and combinatorics of Koornwinder polynomials, but other special functions also made their appearance, in particular Bessel functions, rational solutions of Painlevé equations, the Riemann zeta function, and Airy functions. Most notably there was a lot of emphasis on applications, more so than previous OPSFA meetings: approximation on the real line, cubature on regular polygons, random matrix theory, geometry of Painlevé equations, non-smooth waves, point processes and numerical methods. A public lecture by Andrei Martínez Finkelshtein gave a very entertaining insight into the mathematics of the eye, in particular medical diagnostic analysis and medical imaging of the cornea.

The issue contains papers from participants of the meeting but also from others whose work fits into the topics of the symposium. Moreover, a paper discussing open problems is added. A special issue of Studies in Applied Mathematics, Volume 141, Issue 4, edited by Peter Clarkson and Adri Olde Daalhuis, is dedicated to Orthogonal Polynomials, Special Functions and Applications and contains papers by the plenary speakers of OPSFA14.

There are 18 papers with a total of 480 pages.

We thank everybody involved in the organisation of OPSFA14. We are grateful to all the authors who have published papers in the issue, and give our special thanks to all the referees for providing constructive reviews.

The Guest Editors        

Papers in this Issue:

Open Problems for Painlevé Equations
Peter A. Clarkson
SIGMA 15 (2019), 006, 20 pages [ abs   pdf ]
Solution of an Open Problem about Two Families of Orthogonal Polynomials
Walter Van Assche
SIGMA 15 (2019), 005,   6 pages [ abs   pdf ]
Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant Curvature
Howard S. Cohl, Thinh H. Dang and T.M. Dunster
SIGMA 14 (2018), 136, 45 pages [ abs   pdf ]
Structure Relations of Classical Orthogonal Polynomials in the Quadratic and $q$-Quadratic Variable
Maurice Kenfack Nangho and Kerstin Jordaan
SIGMA 14 (2018), 126, 26 pages [ abs   pdf ]
Inverse of Infinite Hankel Moment Matrices
Christian Berg and Ryszard Szwarc
SIGMA 14 (2018), 109, 48 pages [ abs   pdf ]
Asymptotic Expansions of Jacobi Polynomials for Large Values of $\beta$ and of Their Zeros
Amparo Gil, Javier Segura and Nico M. Temme
SIGMA 14 (2018), 073,   9 pages [ abs   pdf ]
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
Mourad E.H. Ismail, Erik Koelink and Pablo Román
SIGMA 14 (2018), 072, 24 pages [ abs   pdf ]
$d$-Orthogonal Analogs of Classical Orthogonal Polynomials
Emil Horozov
SIGMA 14 (2018), 063, 27 pages [ abs   pdf ]
Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight
Thomas Oliver Conway and Percy Deift
SIGMA 14 (2018), 056, 66 pages [ abs   pdf ]
Quasi-Orthogonality of Some Hypergeometric and $q$-Hypergeometric Polynomials
Daniel D. Tcheutia, Alta S. Jooste and Wolfram Koepf
SIGMA 14 (2018), 051, 26 pages [ abs   pdf ]
Recurrence Relations for Wronskian Hermite Polynomials
Niels Bonneux and Marco Stevens
SIGMA 14 (2018), 048, 29 pages [ abs   pdf ]
On the Strong Ratio Limit Property for Discrete-Time Birth-Death Processes
Erik A. van Doorn
SIGMA 14 (2018), 047,   9 pages [ abs   pdf ]
The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
Paul Terwilliger
SIGMA 14 (2018), 044, 18 pages   [ abs   pdf ]
One of the Odd Zeta Values from $\zeta(5)$ to $\zeta(25)$ Is Irrational. By Elementary Means
Wadim Zudilin
SIGMA 14 (2018), 028,   8 pages   [ abs   pdf ]
Fourier Series of Gegenbauer-Sobolev Polynomials
Óscar Ciaurri and Judit Mínguez
SIGMA 14 (2018), 024, 11 pages   [ abs   pdf ]
Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
Christophe Charlier and Alfredo Deaño
SIGMA 14 (2018), 018, 43 pages   [ abs   pdf ]
Orthogonal Rational Functions on the Unit Circle with Prescribed Poles not on the Unit Circle
Adhemar Bultheel, Ruyman Cruz-Barroso and Andreas Lasarow
SIGMA 13 (2017), 090, 49 pages   [ abs   pdf ]
The Inverse Spectral Problem for Jacobi-Type Pencils
Sergey M. Zagorodnyuk
SIGMA 13 (2017), 085, 16 pages   [ abs   pdf ]

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