Main navigation  Main content
Organizers:
George Andrews  Mathematics, Penn State University  andrews@math.psu.edu 
Richard Askey  Mathematics, University of Wisconsin, Madison  askey@math.wisc.edu 
Carl de Boor  Computer Science, University of Wisconsin, Madison  deboor@cs.wisc.edu 
Arieh Iserles  Applied Math & Theoretical Physics,University of Cambridge  A.Iserles@damtp.cam.ac.uk 
Daniel W. Lozier  Mathematics & Computational Sciences, National Institute of Standards and Technology  lozier@nist.gov 
Willard Miller  Mathematics, University of Minnesota  miller@ima.umn.edu 
Frank W.J. Olver  Institute
for Physical Science & Technology, University of Maryland and Mathematics & Computational Sciences, National Institute of Standards and Technology 
olver@ipst.umd.edu 
Peter Olver  Mathematics, University of Minnesota  olver@ima.umn.edu 
Peter Paule  Research Institute for Symbolic Computation, University of Linz  peter.paule@risc.unilinz.ac.at 
Introduction:
Mathematical tables and handbooks have played a pivotal role in applications and also the development of mathematics itself over the centuries. Now, with the advent of the digital age, the traditional handbook format has become obsolete, and a complete rethinking of the nature and role of mathematical handbooks must be undertaken. The purpose of this program is to formulate, though concrete examples and experiences, the role and character of digital libraries in mathematics, and the mathematical and applied fields that would benefit from such a library. The first serious attempt to address these issues is the ongoing Digital Library of Mathematical Functions (DLMF) project at the National Institute of Standards and Technology (NIST). This workshop will take the DLMF project as a basis for assessing both the state of the art in special function theory, what aspects are of importance in applications, particularly to chemistry and physics, and the experiences gained in this project to formulate recommendations for how digitial libraries of mathematics should be organized, utilized, and developed. We also anticipate the experiences of the DLMF project to provide insight and recomendations for how mathematics should be stored and disseminated over the internet.
Of the currently used handbooks, the most welldeveloped have been those devoted to special functions and their applications. The principal handbooks on special functions, "Higher Transcendental Functions" (the Bateman Project) and the NIST (formerly National Bureau of Standards) "Handbook of Mathematical Functions," are among the most useful, widely consulted technical volumes ever published, but they are now out of date, due to rapid research progress and revolutionary changes in technology. (See http://www.siam.org/siamnews/0398/function.htm for additional information.) Using these as concrete examples of a mathematical digital library, the program will assess recent progress in updating these handbooks and recent advances in the theory and use of special functions, and to point out the areas of research in special functions that hold the most promise and importance for future development, both for theorists and users. In the broader arena, the workshop will aim to use the experience in this particular subject to generate recommendations for further digital library projects in the mathematical sciences and their applications, including, but not limited to, numerical analysis, group theory, signal processing, statistics, linear algebra, partial differential equations, and so on.
See an article by Peter Paule on the DLMF project.
Description:
The IMA workshop will use the DLMF project as a foundation and discuss what more should be done, what areas are incomplete or unrepresented, what are the resulting mathematical, symbolic, numerical and web issues, applications in physics, chemistry, etc., relationships with the Bateman project, and potential for other digital libraries in other mathematical areas. The workshop is to have a very broad outlook, encompassing a wide range of subjects connected with special functions, as well as issues concerning digital libraries and the delivery of mathematics over the internet.
A major portion of this program (7 days) will be assessments of research progress and promising vistas for future research by distinguished experts in the areas of a symptotics, combinatorial functions, statistics, computer algebra, algebraic and group theoretic methods, applications to the physical sciences, orthogonal polynomials, numerical methods, zeta functions & random matrices, Painlevé functions, elliptic functions, elliptic hypergeometric functions and the Heun function group, with the aim of pointing out what is of greatest importance in the theory and applications, and what should be included in digital library projects.
The remainder of the program (3 days) will be devoted to Digital Libraries generally and, specifically, Digital Libraries and the Mathematical Sciences, including the delivery of mathematics over the Internet. It will conclude with a panel on the "Future of Mathematical Digital Libraries," with panelists from the special functions research and users communities, as well as representatives from mathematics societies and government funding agencies.
There will be several discussion sessions to develop specific recommendations for special function topics to be included in future Digital Libraries in Mathematics. Also there will be poster sessions, and several software demonstrations (particularly of computer algebra and numerical packages for special functions), and much of the software will be available during the program for informal use by participants. This program will link with special function related sessions at the Foundations of Computational Mathematics (FoCM'02) meeting that will be hosted by the IMA, August 515, 2002.
The program is meant for researchers in the theory and computation of special functions (definitely including people new to the field who are looking for the most promising areas for future research), for users of special functions, and for persons interested in the delivery of mathematics over the Internet.
Week 1  July 2226  Monday  Tuesday  
Week 2  July 29August 2  Monday  Tuesday 
MONDAY,
JULY 22 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:00 am  Coffee and Registration 
Reception Room EE/CS 3176 

8:50 am  Douglas
N. Arnold IMA Director 
Welcome and Introduction  


9:00 am  Richard
Askey University of Wisconsin 
Introduction: The Role of Handbooks of Special Functions  
9:15 am  Dan
Lozier National Institute of Standards and Technology 
Development of a New Handbook and Web Site of Properties of Special Functions Slides: html pdf powerpoint 

10:05 am 


10:15 am  Coffee Break  Reception Room EE/CS 3176  
10:45 am  Ronald
F. Boisvert National Institute of Standards and Technology 

11:35 am 


11:45 am 
Lunch
Break




1:30 pm  Frank
W.J. Olver National Institute of Standards and Technology 

2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Michael
Berry University of Bristol 

3:50 pm 


4:00 pm  IMA
Tea/Reception A variety of appetizers and beverages will be served. 
IMA East, 400 Lind Hall  
TUESDAY,
JULY
23
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  


9:00 am  Dennis
Stanton University of Minnesota 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
10:30 am  David M. Bressoud Macalester College 

11:20 am 


11:30 am 
Lunch
Break


1:30 pm  Alexander
Berkovich University of Florida 
Partitions with gap conditions: some old and new results  
2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
Theme: Group Theoretic Methods  
3:00 pm  Willard
Miller University of Minnesota 

3:50 pm 


4:00
pm

Panel Discussion Participants have the opportunity to pose to Stanton, Bressoud, Berkovich, and Miller any questions or suggestions that may have arisen from their talks or that circle of ideas. 

WEDNESDAY,
JULY
24 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Computer Algebra: Identity Verification, Summation Methods, Special Packages  
9:00 am  George
E. Andrews Pennsylvania State University 
What is needed in Computer Algebra Packages for Mathematical Research!  
9:50 am 


10:00 am  Peter
Paule University of Linz 

10:50 am 


11:00 am  Coffee Break  Reception Room EE/CS 3176  
11:30 am  Doron
Zeilberger Rutgers University 
The General Future of Special Functions  
12:20 pm 


12:30 pm 
Lunch
Break


2:00 pm  Otmar
Scherzer University of Innsbruck 
Case examples of Special Functions in Analysis and Numerics  
2:50 pm  Discussion  
3:00 pm  Coffee Break  Reception Room EE/CS 3176  
3:30 pm  Frédéric
Chyzak INRIA 

4:00 pm  Christian Krattenthaler Universitat Wien 
Matematica
Slides:
hyp.nb
hyp1.nb
hypq.nb 

4:30 pm  Axel
Riese J. Kepler University, Linz 
Computer Proofs of Hypergeometric Summation Identities and Partition Analysis  
5:00 pm 


THURSDAY,
JULY
25 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Algebraic Methods: Lie Groups, Quantum Groups, Quasiexactly Solvable Methods  
9:00 am  Arieh
Iserles University of Cambridge 
Lie group methods for highly oscillatory differential equations  
9:50 am 


10:00 am  Tom
H. Koornwinder Universiteit van Amsterdam 

10:50 am 


11:00 am  Coffee Break  Reception Room EE/CS 3176  
11:30 am  Alexander
Turbiner National University of Mexico 
Algebraic Approaches: QuasiExactlySolvable Problems (Liealgebraic theory of polynomial solutions of differential and finitedifference linear equations) abstract.pdf abstract.ps 

12:20 pm 


12:30 pm 
Lunch
Break




2:00 pm  Alexander
Its Indiana University Purdue University Indianapolis 
Integrable Systems and Integrability  
2:50 pm 


3:00 pm  Coffee Break  Reception Room EE/CS 3176  
3:30 pm  Pavel
Bleher Indiana University Purdue University Indianapolis 
Double scaling limits in random matrix models and orthogonal polynomials: RiemannHilbert approach  
4:20 pm 


6:00 pm  Workshop Dinner  Bangkok
Thai Restaurant 425 13th Ave. SE Minneapolis, MN 

FRIDAY,
JULY
26 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30am  Coffee  Reception Room EE/CS 3176  
Theme: Orthogonal Polynomials  
9:00 am  Richard
Askey University of Wisconsin 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
10:30 am  Charles
F. Dunkl University of Virginia 

11:20 am 


Theme: Statistics  
1:30 pm 
Donald Richards University of Virginia 
Computers and special functions in multivariate statistical analysis  
2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Ingram
Olkin Stanford University 
Interface Between Statistics and Special Functions  
3:50 pm 


4:00 pm 


MONDAY,
JULY 29 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Numerical Methods: Orthogonal Polynomials  
9:00 am  Walter
Gautschi Purdue University 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
Theme: Numerical Methods: General Special Functions, Software  
10:30 am  Nico
M. Temme CWI 
Slides: pdf 

11:20 am 


11:30 pm 
Lunch
Break


1:30 pm  Oleg
Marichev Wolfram Research, Inc. 
www.functions.wolfram.com  The web's most comprehensive site about special functions 

2:00 pm  Edgardo
S. ChebTerrab Simon Fraser University 
Special functions & Maple  
2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Cleve
Moler The MathWorks Inc. 
The MathWorks Inc. Special Functions in MATLAB What do we have and what are we missing?  
3:30 pm 


7:00 pm 


TUESDAY,
JULY
30
All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Zeta Functions & Random Matrices  
9:00 am  Andrew
M. Odlyzko University of Minnesota 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
10:30 am  Peter
A. Clarkson University of Kent at Canterbury 
The Painleve equations  nonlinear special functions Expanded version of the talk and figures: SF02L.pdf SF02L.ps plots.pdf plots.ps 

11:20 am 


11:30 pm 
Lunch
Break


Theme: Elliptic Functions  
1:30 pm  Peter
L. Walker American University of Sharjah 
The elliptic functions of Jacobi and Weierstrass  
2:20 pm 


2:30 pm  William
P. Reinhardt University of Washington 
New and old addition theorems and Landen identities for Jacobian elliptic functions: do these indeed give rise to "novel" solutions for nonlinear PDEs?  
3:20 pm 


3:30 pm  Coffee Break  Reception Room EE/CS 3176  
4:00 pm  Vyacheslav P. Spiridonov Joint Institute for Nuclear Research, Russia 

4:50 pm 


5:00 pm 


WEDNESDAY,
JULY
31 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Mathieu, Lamé, and Spheroidal Wave Functions  
9:00 am  Hans
W. Volkmer University of Wisconsin 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
Theme: Digital Library Infrastructure for Mathematical DL's: Display and Manipulation, Meta Data, Searching  
10:30 am  Andrew
M. Odlyzko University of Minnesota 
The new (and of necessity digital) libraries for mathematics 

11:20 am 


11:30 pm 
Lunch
Break


1:30 pm  Abdou
Youssef The George Washington University 
Search Systems for Mathematical Equations pdf ps  
2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Patrick
Ion Math Reviews 
Mathematics on the Web  
3:50 pm 


4:00 pm 


THURSDAY,
AUGUST
1 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: Digital Library Infrastructure for Mathematical DL's: Display and Manipulation, Meta Data, Searching (continued)  
9:00 am  Bruce
R. Miller NIST 
Representation, display and manipulation of mathematics on the Web pdf ps Slides: pdf 

9:50 am 


10:00 am  Coffee Break  Reception Room EE/CS 3176  
10:30 am  Bonita
V. Saunders National Institute of Standards and Technology 
Interactive 3D Visualizations of High Level Functions in a Mathematical Digital Library  
11:20 am 


11:30 pm 
Lunch
Break


Theme: Theorema  
1:30 pm  Bruno
Buchberger Johannes Kepler University 

2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Carsten
Schneider University of Linz 

3:30 pm 


6:00 pm  Workshop Dinner  Mangia
Restaurant 1501 University Ave. in Dinkytown Dome 

FRIDAY,
AUGUST
2 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:30 am  Coffee  Reception Room EE/CS 3176  
Theme: What is Needed?  
9:00 am  Richard
Askey University of Wisconsin 
Assessment of DLMF (Digital Library of Mathematical Functions) 

9:30 am 


9:40 am  Mourad
Ismail University of South Florida 

10:30 am 


10:40 am  Coffee Break  Reception Room EE/CS 3176  
11:10 am  Dennis
Stanton University of Minnesota 
Comments on Combinatorics and Special Functions 

11:40 am 


11:50 am 
Dan
Lozier
Peter
A. Clarkson 
What can the SIAM OPSF Activity Group do for you?  
12:00 pm 


12:10 pm 
Lunch
Break


Theme: Panel on Future of Mathematical Digital Libraries: Funding, Maintenance, Copyright, Publication  
2:00 pm 
Panel Discussion 

3:30 pm  Coffee Break  Reception Room EE/CS 3176  
4:00 pm 

Week 1  July 2226  Monday  Tuesday  
Week 2  July 29August 2  Monday  Tuesday 
Name

Department  Affiliation 

George E. Andrews  Mathematics  Penn State 
Richard A. Askey  Mathematics  University of WisconsinMadison 
Alex Berkovich  Mathematics  University of Florida 
Michael Berry  Physics  University of Bristol 
Pavel Bleher  Mathematics  Indiana University Purdue University 
Ronald F. Boisvert  Mathematical and Computational Sciences  NIST 
David M. Bressoud  Mathematics and Computer Science  Macalester College 
Bruno Buchberger  Research Institute for Symbolic Computation  Johannes Kepler University 
Bille C. Carlson  Mathematics and Ames Laboratory  Iowa State University 
Jamylle Carter  Institute for Mathematics & its Applications  
Edgardo S. ChebTerrab  Centre for Experimental & Construct. Mathematics  Simon Fraser University 
Christine Cheng  Institute for Mathematics & its Applications  University of Minnesota 
Jacob Stordal Christiansen  Mathematics  University of Copenhagen 
Frederic Chyzak  INRIA Rocquencourt  
Charles W. Clark  Electron and Optical Physics  NIST 
Peter A. Clarkson  Institute of Mathematics and Statistics  University of Kent at Canterbury 
Charles Conley  Mathematics  University of North Texas 
Steven Benjamin Damelin  Mathematics  Georgia Southern University 
Carl de Boor  Computer Science and Mathematics  University of WisconsinMadison 
Charles F. Dunkl  Mathematics  University of Virginia 
Michael Efroimsky  University of Minnesota  Institute for Mathematics and its Applications 
Kristina Garrett  Carleton College  
Walter Gautschi  Computer Science  Purdue University 
Amparo Gil  Mathematics  Universidad Autonoma de Madrid 
John Hall  Mathematics  University of Minnesota 
Hazem Hamdan  Mathematics  Unhiversity of Minnesota 
Patrick Ion  Associate Editor  Math Reviews 
Arieh Iserles  Applied Mathematics and Theoretical Physics  University of Cambridge 
Mourad Ismail  Mathematics  University of South Florida 
Alexander Its  Science  Indiana UniversityPurdue University Indianapolis 
Sara Jane Johnston  Mathematics  University of the Witwatersrand 
Tom Koornwinder  Kortewegde Vries Institute for Mathematics  Universiteit van Amsterdam 
Christian Krattenthaler  Institut fur Mathematik  Universitat Wien 
Arno Kuijlaars  Mathematics  Katholieke Universiteit Leuven/ from CWI 
James Licari  Digital Technology Center  University of Minnesota 
Jose L. Lopez  Mathematics and Informatics  Public University of Navarra 
Jeremy Lovejoy  Mathematics  University of Wisconsin, Madison 
Daniel W. Lozier  Mathematical and Computational Sciences  NIST 
Robert S. Maier  Mathematics and Physics  University of Arizona 
Elizabeth L. Mansfield  Institute of Mathmematics and Statistics  University of Kent at Canterbury 
Oleg Marichev  Information Resources  Wolfram Research Inc. 
Bruce R. Miller  National Institute of Standards and Technology  NIST 
Willard Miller  Mathematics  University of Minnesota 
Robert Miner  Design Science, Inc.  
Cleve Moler  Chairman and Chief Scientist  The MathWorks Inc. 
Mahdi Nezafat  Electrical and Computer Engineering  University of Minnesota 
Nilima Nigam  Mathematics  McGill University 
Andrew Odlyzko  Digital Technology Center  University of Minnesota 
Adri Olde Daalhuis  Mathematics and Statistics  Edinburgh University 
Ingram Olkin  Statistics  Stanford University 
Frank W. J. Olver  Institute for Physical Science & Technology  University of Maryland 
Peter J. Olver  Mathematics  University of Minnesota 
JeongSoo Park  Statistics  Chonnam National University/SRCCS 
Peter Paule  Institute for Symbolic Computation  University of Linz 
Georg Regensburger  Institut für Informatik  Universität Innsbruck 
Vic Reiner  Mathematics  University of Minnesota 
William P. Reinhardt  Chemistry Box 351700  University of Washington 
Donald Richards  Statistics  University of Virginia 
David A. Richter  Mathematics  Southeast Missouri State University 
Axel Riese  Research Institute for Symbolic Computation  J. Kepler University Linz 
Bonita V. Saunders  Mathematical and Computational Sciences  NIST 
Otmar Scherzer  Applied Mathematics  Dept. of Computer Science  University of Innsbruck 
Michael Schlosser  Mathematics  University of Vienna 
Carsten Schneider  Research Institute for Symbolic Computation  University of Linz 
Javier Segura  Mathematics  Universidad Carlos III de Madrid 
Ajay Kumar Shukla  Mathematics / ASHD  S.V. Regional College of Engineering & Technology 
Andrew V. Sills  Mathematics  Penn State University 
Vyacheslav P. Spiridonov  Bogoliubov Laboratory of Theoretical Physics  Joint Institute for Nuclear Research 
Dennis Stanton  Mathematics  University of Minnesota 
Nico M. Temme  Analysis  CWI 
Paul Terwilliger  Mathematics  University of Wisconsin 
Alexander Turbiner  Instituto de Ciencias Nucleares  National University of Mexico 
Hans W. Volkmer  Mathematical Sciences  University of Wisconsin 
Peter L. Walker  
S. Ole Warnaar  Mathematics and Statistics  The University of Melbourne 
Jim Wilson  Mathematics  Iowa State University 
Abdou Youssef  Computer Science  The George Washington University 
Doron Zeilberger  Mathematics  Rutgers, The State University of New Jersey 
Foundations
of Computational Mathematics 2002 (FoCM'02) August 514, 2002
20022003 Program: Optimization