
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, nonsmooth 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 BurchnallType 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 ]

QuasiOrthogonality 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 DiscreteTime BirthDeath Processes

Erik A. van Doorn
SIGMA 14 (2018), 047, 9 pages [ abs
pdf ]

The $q$Onsager Algebra and the Universal AskeyWilson 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 GegenbauerSobolev 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 CruzBarroso and Andreas Lasarow
SIGMA 13 (2017), 090, 49 pages [ abs
pdf ]

The Inverse Spectral Problem for JacobiType Pencils

Sergey M. Zagorodnyuk
SIGMA 13 (2017), 085, 16 pages [ abs
pdf ]

