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

Special Issue on Orthogonal Polynomials, Special Functions and Applications

The Guest Editors for this special issue are

Howard Cohl (National Institute of Standards and Technology, Gaithersburg, Maryland, USA)
Diego Dominici (State University of New York at New Paltz, USA)
Tom Koornwinder (University of Amsterdam, The Netherlands)
Victor Moll (Tulane University, New Orleans, Louisiana, USA)
Walter Van Assche (University of Leuven, Belgium)

The issue is related to the 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA13), held at the National Institute of Standards and Technology (NIST), Gaithersburg, Maryland, USA, June 1–5, 2015. The issue contains papers from participants of the meetings but also from others whose work fits into the topics of the symposium. Four of the plenary speakers wrote a contribution for this special issue (Charles Dunkl, Mourad Ismail, Teresa Pérez, and Wadim Zudilin) and there is a report from the open problem session of OPSFA-13. There are 28 papers with a total of 555 pages. We would like to thank the chairs of the scientific committee of OPSFA-13, and in particular Daniel W. Lozier of NIST, for the organization of the meeting.

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:

On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight
Marco Bertola and Alexander Tovbis
SIGMA 12 (2016), 118, 50 pages   [ abs   pdf ]
Multivariate Orthogonal Polynomials and Modified Moment Functionals
Antonia M. Delgado, Lidia Fernández, Teresa E. Pérez and Miguel A. Piñar
SIGMA 12 (2016), 090, 25 pages   [ abs   pdf ]
A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
Richard Chapling
SIGMA 12 (2016), 079, 20 pages   [ abs   pdf ]
Orthogonal Polynomials Associated with Complementary Chain Sequences
Kiran Kumar Behera, A. Sri Ranga and A. Swaminathan
SIGMA 12 (2016), 075, 17 pages   [ abs   pdf ]
Report from the Open Problems Session at OPSFA13
Edited by Howard S. Cohl
SIGMA 12 (2016), 071, 12 pages   [ abs   pdf ]
Periodic GMP Matrices
Benjamin Eichinger
SIGMA 12 (2016), 066, 19 pages   [ abs   pdf ]
Multidimensional Toda Lattices: Continuous and Discrete Time
Alexander I. Aptekarev, Maxim Derevyagin, Hiroshi Miki and Walter Van Assche
SIGMA 12 (2016), 054, 30 pages   [ abs   pdf ]
Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
Dmitrii Karp and Elena Prilepkina
SIGMA 12 (2016), 052, 23 pages   [ abs   pdf ]
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Emil Horozov
SIGMA 12 (2016), 050, 14 pages   [ abs   pdf ]
Shell Polynomials and Dual Birth-Death Processes
Erik A. van Doorn
SIGMA 12 (2016), 049, 15 pages   [ abs   pdf ]
Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
Luc Vinet and Alexei Zhedanov
SIGMA 12 (2016), 048, 14 pages   [ abs   pdf ]
The Asymptotic Expansion of Kummer Functions for Large Values of the $a$-Parameter, and Remarks on a Paper by Olver
Hans Volkmer
SIGMA 12 (2016), 046, 22 pages   [ abs   pdf ]
Polynomial Sequences Associated with the Moments of Hypergeometric Weights
Diego Dominici
SIGMA 12 (2016), 044, 18 pages   [ abs   pdf ]
One-Step Recurrences for Stationary Random Fields on the Sphere
R.K. Beatson and W. zu Castell
SIGMA 12 (2016), 043, 19 pages   [ abs   pdf ]
Zeros of Quasi-Orthogonal Jacobi Polynomials
Kathy Driver and Kerstin Jordaan
SIGMA 12 (2016), 042, 13 pages   [ abs   pdf ]
Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation
Michael J. Schlosser and Meesue Yoo
SIGMA 12 (2016), 039, 21 pages   [ abs   pdf ]
Bôcher Contractions of Conformally Superintegrable Laplace Equations
Ernest G. Kalnins, Willard Miller Jr. and Eyal Subag
SIGMA 12 (2016), 038, 31 pages   [ abs   pdf ]
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples
Nizar Demni
SIGMA 12 (2016), 035, 13 pages   [ abs   pdf ]
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
Charles F. Dunkl
SIGMA 12 (2016), 033, 27 pages   [ abs   pdf ]
Classes of Bivariate Orthogonal Polynomials
Mourad E.H. Ismail and Ruiming Zhang
SIGMA 12 (2016), 021, 37 pages   [ abs   pdf ]
Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
Clotilde Martínez and Miguel A. Piñar
SIGMA 12 (2016), 020, 11 pages   [ abs   pdf ]
Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures
Erik Koelink and Pablo Román
SIGMA 12 (2016), 008,  9 pages   [ abs   pdf ]
Hankel Determinants of Zeta Values
Alan Haynes and Wadim Zudilin
SIGMA 11 (2015), 101,  5 pages   [ abs   pdf ]
Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$
Boris Feigin, Ayumu Hoshino, Masatoshi Noumi, Jun Shibahara and Jun'ichi Shiraishi
SIGMA 11 (2015), 100, 21 pages   [ abs   pdf ]
Rigorous Asymptotics for the Lamé and Mathieu Functions and their Respective Eigenvalues with a Large Parameter
Karen Ogilvie and Adri B. Olde Daalhuis
SIGMA 11 (2015), 095, 31 pages   [ abs   pdf ]
Certain Integrals Arising from Ramanujan's Notebooks
Bruce C. Berndt and Armin Straub
SIGMA 11 (2015), 083, 11 pages   [ abs   pdf ]
Moments and Legendre-Fourier Series for Measures Supported on Curves
Jean B. Lasserre
SIGMA 11 (2015), 077, 10 pages   [ abs   pdf ]
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions
Bartosz Langowski
SIGMA 11 (2015), 073, 17 pages   [ abs   pdf ]

Special Issues in SIGMA

SIGMA main page