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Program of the Conference Foreward Dear Friends, Welcome to the International Conference on Orthogonal Polynomials and q-series (May 10—12, 2015) at University of Central Florida, Orlando, Florida. This conference is dedicated to Professor Mourad Ismail on his 70th birthday. The main themes are two topics in which Mourad has made fundamental contributions. The organizing committee would like to extend sincere thanks for your coming to the conference held in sunny Orlando. Many of you came from different places far and near. Special welcome to the European, Middle Eastern and Chinese participants for making such a long journey to be with us and share this celebration and conference. We hope you will enjoy the stay and take advantage of being in the great Orlando area and to visit our world class attractions and some neighboring sites. Due to your presence and participation, we believe that the conference will be successful, and it will promote and enhance collaborations/interactions among scholars from different areas, both geographically and mathematically. Publication of the Proceeding of the Conference is planned. We thank Linda Perez-Rodriguez, Janice Burns and Doreen Goulding for their help. We would like to express our acknowledgement to the following organizations/units for their financial support: University of Central Florida King Saud University College of Science, UCF Department of Mathematics, UCF Our acknowledgement also goes to Elsevier Publisher and Pearson Higher Education. Conference organization committee International Conference on Orthogonal Polynomials and q-Series May 10--12, 2015, University of Central Florida Dedicated to Professor Mourad Ismail Sunday Morning (May 10, 2015) 7:00—1:30 Registration Chaired by Xin Li 8:30—8:40 Opening 8:40—9:30 Richard Askey (University of Wisconsin-Madison) Some of what I owe to Mourad Ismail and some elementary inequalities, both old and new 9:35—10:15 Roderick Wong (City University of Hong Kong) Asymptotics and Orthogonal Polynomials 10:15—10:35 Break Chaired by Roderick Wong 10:35—11:15 Erik Koelink (Radboud Universiteit) An explicit family of matrix-valued orthogonal polynomials in the q-Askey scheme 11:20—12:00 Tom Koornwinder (University of Amsterdam) Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators Sunday Afternoon (May 10, 2015) Chaired by Dennis Stanton 1:30—2:10 Victor H. Moll (Tulane University) A collection of questions coming from the evaluation of integrals 2:15--2:55 Frank Garvan (University of Florida) Transformation Properties of Dyson's Rank Function 2:55—3:10 Break Parallel Session 1, chaired by Victor H. Moll 3:10—3:40 Martin Muldoon (York University) Monotonicity properties of zeros of ultraspherical polynomials 3:45—4:15 Alexey Kuznetsov (York University) The double sine function and its application in Analysis and Probability 4:20—4:50 Francisco Marcellan (Universidad Carlos III de Madrid) Multiple Geronimus transformations Parallel Session 2, chaired by Frank Garvan 3:10—3:40 Plamen Simeonov (University of Houston Downtown) Formula and identities for the Askey-Wilson Operator 3:45—4:15 Robert Maier (University of Arizona) The Ince Equation and its Solutions 4:20—4:50 Changgui Zhang (University of Lille) On the Mock-Theta behavior of Appell-Lerch series 5:50 Group photo 6:00 Reception Monday Morning (May 11, 2015) 7:00—1:30 Registration Chaired by Richard Askey 8:30—9:20 Dennis Stanton (University of Minnesota) A small slice of Mourad’s work 9:25—10:05 George Andrews (The Pennsylvania State University) Bressoud's easy proof of the Rogers-Ramanujan identities and Bressoud polynomials 10:05—10:25 Break Parallel Session 1, chaired by Luc Vinet 10:25—10:55 Paul Terwilliger (University of Wisconsin-Madison) Lowering-rasing triples of linear transformations 11:00—11:20 Christophe Vignat (University of Orsay, Tulane University) A symbolic approach to multiple zeta values at the negative integers 11:20—11:40 Atul Dixit (Tulane University) Zagier polynomial, their asymptotics and exact formulas 11:40—12:00 Christopher M. Jennings-Shaffer (University of Florida) A few exotic Bailey slater smallest parts partition functions Parallel session 2, chaired by Tom Koornwinder 10:25—10:55 Bruce Berndt (University of Illinois at Urbana-Champaign) Mathematical connections between Ramanujan and Hardy in Ramanujan’s earlier notebooks and lost notebook 11:00—11:20 Karl Dilcher (Dalhousie University) High-order convolutions for Bernoulli and Euler polynomials 11:20—11:40 Ahmad El-Guindy (Texas A&M University at Qatar) Atkin’s orthogonal polynomial and associated Jacobi polynomials Monday Afternoon (May 11, 2015) Chaired by Erik Koelink 1:30—2:10 Willi Freeden (University of Kaiserslautern) Euler summation and Shannon sampling 2:15—2:55 Ruiming Zhang (Northwest A&F University) On Fourier transform and q-spherical functions 2:55—3:10 Break Parallel session 1, chaired by George Andrews 3:10—3:40 Yang Chen (University of Macau), Talk cancelled Hankel determinants, singular perturbation, greater to lesser Painleve III 3:45—4:15 Dan Dai (City University of Hong Kong) Painleve III asymptotics of Hankel determinants for a singular perturbed Laguerre weight 4:20—4:50 Alexander Tovbis (University of Central Florida) Asymptotics of orthogonal polynomials with complex varying weight: critical point behavior and the Painleve equation 4:55—5:25 Roberto Costas-Santos (Universidad de Alcala) Extensions of discrete polynomials beyond the orthogonality Parallel session 2, chaired by Willi Freeden 3:10—3:40 Ahmed Zayed (Depaul University) Prolate spherical wave functions and reproducing-kernel Hilbert spaces 3:45—4:15 Howard Cohl (NIST) Newtownian potential theory and superintegrability on hyperspheres 4:20—4:50 Peter Paule (Johannes Kepler University Linz) The concrete Tetrahedron for special functions 4:55—5:25 Tim Huber (University of Texas Pan American) On a level 17 analogue of the Rogers-Ramanujan continued fraction 6:30—9:30 Banquet Tuesday Morning (May 12, 2015) Parallel session 1, chaired by Paul Nevai 8:30—9:00 Sarah Post (University of Hawaii) q-rotations and Krawtchouk polynomials 9:05—9:35 Igor Pritsker (Oklahoma University) Expected number of real zeros of random orthogonal polynomials 9:40—10:10 Emily Leven The rational Shuffle conjectures Parallel session 2, chaired by Ruiming Zhang 8:30—9:00 Xin Li (University of Central Florida) Some New Results on Bernstein-type Inequalities for a Rational Functions 9:05—9:35 Armin Straub (University of Illinois at Urbana-Champaign) On a q-analog of the Apery numbers 9:40—10:10 Jiang Zeng (University Claude Bernard Lyon ) Some combinatorial aspects of 2D-Hermite polynomials and 2D-Laguerre polynomials 9:40—10:10 Break Chaired by Zuhair Nashed 10:30—11:10 Paul Nevai (STRSOH) Some inequalities in approximation theory 11:15—11:55 Luc Vinet (University of Montreal) A q-generalization of the Bannai-Ito polynomials and the quantum Superalgebra osp_q(1|2) 11:55 closing Titles and Abstracts for the International Conference on Orthogonal Polynomials and q-Series May 10 - 12, 2015, University of Central Florida Richard Askey ([email protected]) { University of WisconsinMadison Some of what I owe to Mourad Ismail and some elementary inequalities, both old and new Abstract: Through the years Mourad has come up with some gems which have been very useful and/or surprising to me. I will describe a few of these. The second part of the talk will be completely different, no orthogonal polynomials or q-series, just a few inequalities involving polynomials and some consequences. George Andrews ([email protected]) { The Pennsylvania State University Bressoud's easy proof of the Rogers-Ramanujan identities and Bressoud polynomials Abstract: In 1974, a multiple series generalization of the Rogers-Ramanujan identities was proved. In 1983, David Bressoud published \An Easy Proof of the Rogers-Ramanujan identities." The main body of the paper provided exactly what was promised in the title. The paper concludes with a multiple series of generalization that has multiple suprises beneath the surface. We hope to illuminate some these surprises. Bruce Berndt ([email protected]) { University of Illinois at Urbana-Champaign Mathematical Connections Between Ramanujan and Hardy in Ramanujan's Earlier Notebooks and Lost Notebook Abstract: The joint work of Hardy and Ramanujan in their published papers continues to have a huge impact on contemporary research in number theory, combinatorics, and analysis. We do not discuss these contributions in this talk, but instead focus on the impact that each had on the other as evinced in several entries in the notebooks and lost notebook. The famous unsolved circle, divisor, and extended divisor problems, and the Riemann zeta function are featured. Most of this lecture is based on joint work with Atul Dixit, Sun Kim, Arindam Roy, and Alexandru Zaharescu. M. El Bachraoui ([email protected]) { UAE University On polynomiality of q-binomial coefficients Abstract: We provide a characterization of the polynomiality of the q-binomial coefficients and therefore also a characterization of congruence for the binomial coefficients. As an application we give a simple proof for a recent theorem by Guo and Krattenthaler. Yang Chen ([email protected]) { University of Macau, China Hankel determinants, singular perturbation, greater to lesser Painleve III Abstract: In this talk, I will discuss Hankel determinant generated by a Laguerre weight multiplied by exp(−t=x); t > 0, inducing an infinitely fast 0 at the origin. For finite n, the Hankel determinant, is expressed in terms a finite n Painleve III. Under double scaling where n ! 1 and t ! 0, such that s := 2nt is finite, the original PIII becomes a lesser PIII. The large s asymptotic expansion of the scaled, and in some sense, infinite determinant is obtained. This talk ends with a discussion of the constant term in the large s expansion.
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