Volume 4, Number 5




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-                                                                     -
-                                           September 15, 1997        -
-      O P - S F   N E T                    Volume 4, Number 5        -
-      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~        -
-      Editors:                                                       -
-      Tom H. Koornwinder                   thk@wins.uva.nl           -
-      Martin Muldoon                       muldoon@yorku.ca          -
-                                                                     -
-      The Electronic News Net of the SIAM Activity Group             -
-      on Orthogonal Polynomials and Special Functions                -
-                                                                     -
-                 Please send contributions to:  poly@siam.org        -
-                 & address changes to:  poly-request@siam.org        -
-                                                                     -
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Today's Topics
     1. Renewal of our Activity Group's charter
     2. Report on Stanford Minisymposium "Handbooks for Special Functions
             and the World Wide Web"
     3. Bill Miller appointed IMA Director
     4. VIII Simposium sobre Polinomios Ortogonales y Aplicaciones,
             Sevilla - update
     5. Meeting on Symmetries and Integrability of Difference Equations
     6. NIST Digital Library of Mathematical Functions
     7. Student membership in SIAM
     8. Updated booklist
     9. Book on Mehler-Fock type transform
    10. Proceedings of the Organic Mathematics Workshop
    11. Rivlin Festschrift
    12. Book on Logarithmic Potentials with External Fields
    13. Maple procedure rec2ortho
    14. Krawtchouk Polynomials Home Page
    15. Changes of Address, WWW Pages, etc.
    16. Obtaining back issues of OP-SF Net and submitting contributions
             to OP-SF Net and Newsletter


Calendar of events:                                      see issue/topic:
1997
September 22-26: VIII Simposium sobre Polinomios Ortogonales y
Aplicaciones, Sevilla, Spain            3.5 #5, 4.2 #4, 4.3 #5 and 4.5 #4

1998
March 22-28: Meeting on Applications and Computation of Orthogonal
Polynomials, Oberwolfach, Germany                                  4.3 #6
May 16-22: Symmetries and Integrability of Difference Equations,
         Sabaudia, Italy                                           4.5 #5
July 13-17: SIAM Annual Meeting, Toronto, Canada



Topic #1   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Allison Bogardo <bogardo@siam.org>
Subject: Charter renewal of Activity Group

Charles Dunkl, chair of our Activity Group, received the following
message from Allison Bogardo:

     Dear Charles:

     I am pleased to advise you that the SIAM Council and Board of
     Trustees approved the renewal of the charter for the
     SIAM Activity Group on Orthogonal Polynomials and Special
     Functions.  The charter is for a three-year period beginning
     January 1, 1999 and ending December 31, 2001.

     We will be in touch with you in the spring of 1998 to begin work on
     your activity group ballot.  In the meantime, if there is any other
     way we can be of assistance to you and your activity group, please
     do not hesitate to be in touch with me.

     Thank you.

     Allison Bogardo
     bogardo@siam.org



Topic #2   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Willard Miller <miller@ima.umn.edu>
Subject: Report on Stanford Minisymposium "Handbooks for Special
             Functions and the World Wide Web"

The Activity Group on Orthogonal Polynomials and Special Functions
sponsored the Minisymposium "Handbooks for Special Functions and the World
Wide Web" that was held on July 14, 1997 at the SIAM Annual Meeting at
Stanford University. The principal handbooks on special 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.
The minisymposium was organized by Dick Askey and Willard Miller, and
featured talks by representatives of the groups that are proposing to
update the Bateman Project (Mourad Ismail) and Abramowitz & Stegun (Dan
Lozier), respectively, a presentation on the development of a Mathematica
Special Functions Handbook (Olag Marichev and Paul Wellin), and an
assessment of the historical influence of special functions handbooks
(Dick Askey), followed by a general discussion.

Willard Miller chaired the session and started with some desirable
criteria for handbooks: 1) Present, codify and organize the principal
results and tools in appropriate parts of the field of special functions.
Provide insight into the structure of the theory. 2)  Provide easy
accessibility for users. 3) Ensure long term impact. Do carefully
(accurately) and guided by the most knowledgeable experts in the field.
Make easy to update.

Dan Lozier talked about the planning for publication on the World Wide Web
of a modernized and updated revision of the NBS Handbook of Mathematical
Functions, first published in 1964. The authoritative status of the
original publication is to be preserved by enlisting the aid of qualified
mathematicians and scientists. However, there will be increased practical
emphasis on formulas, graphs and numerical evaluation through the
provision of interactive capability to permit generation of tables and
graphs on demand. The "handbook" will be available at a Web site and will
involve a digital library. (Editor's Note: See Topic #6 below for further
information on this project.)

Mourad Ismail discussed plans for updating the Bateman project, both to
reflect progress made on topics covered in the original (written in the
early 1950's) and to add topics of current importance that were not in the
initial project. In particular, the plan is for major additions on one and
multi-variable orthogonal polynomials and on q-series. Mourad emphasized
the importance of involving leading experts in the project. The plan is
that the update should be published in a paper version, with formulas (and
corrections)  available via ftp or on a Web site. One of the arguments
that he presented for a paper version was that many third world
mathematicians and users of mathematics would not have access to a
Web-based product. Cambridge University Press has shown interest in the
project and some funding has been received from the National Security
Agency. Major funding is being sought from the National Science
Foundation.

Oleg Marichev presented current work on the Mathematica Interactive
Special Functions Handbook. The Wolfram Research representatives
emphasized the importance of using recent Web-based technological
developments in a handbook project. Their concept was to have a paper
version of the handbook and a World Wide Web version. On the Web version
search engines could be used, formulas could be down-loaded, manipulated
with Mathematica, and data could be generated and plotted. Hyperlinks
could be used to link formulas with the original reference where they are
derived. Updating and correcting would be simple on the Web. Their message
was that the Mathematica system should be used as the underlying system
for an update of either the NBS or the Bateman project.

Dick Askey talked about the influence, for good or ill, of special
function handbooks through the decades. Many of his examples illustrated
the value of involving leading researchers in these projects. Their input
is critical in deciding what material to include and how to present it.

The issued raised at the Minisymposium are of importance for all in the
special functions user community. The need for updating and codifying the
principal results of the theory are clear, but the sources of funding and
the optimal delivery system are not yet determined. Clearly, special
function handbooks will continue to be produced. If the special functions
research community is to have much influence on their content, we need to
resolve these issues now.

Willard Miller, Jr.



Topic #3   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <muldoon@yorku.ca>
Subject: Bill Miller appointed IMA Director

Bill Miller, our Group's Program Director, has been chosen to succeed
Avner Friedman as Director of the Institute for Mathematics and its
Applications (IMA), University of Minnesota, for a five-year term
beginning September 1, 1997.  The IMA was established in 1982 by the U.S.
National Science Foundation, as a result of a national competition. Its
mission is to close the gap between theory and its applications by
identifying problems and areas of mathematical research needed in other
sciences and by encouraging the participation of mathematicians in these
areas of application.

Professor Miller is a mathematical physicist.  His research involves the
use of symmetry methods, in particular Lie groups and Lie algebras, in the
analysis of the structure of physical theories. He has written extensively
on topics in special function theory, separation of variables, and quantum
algebras.

Willard Miller has had a long association with the IMA.  He was the head
of the School of Mathematics at Minnesota in 1979 when the proposal for
the IMA was made, and he played a major role in bringing the IMA to
Minnesota.  He became Associate Director of the IMA in 1987 and served in
that position for seven years, before becoming Associate Dean for Finance
and Planning of the Institute of Technology at the University of
Minnesota.

We congratulate Bill on this important appointment and wish him every
success in his leadership of the IMA.

(Much of the above information is taken from the IMA web site:
http://www.ima.umn.edu/).



Topic #4   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Walter Van Assche <walter@wis.kuleuven.ac.be>
Subject: VIII Simposium sobre Polinomios Ortogonales y Aplicaciones,
             Sevilla - update

The VIII Simposium sobre Polinomios Ortogonales y Aplicaciones
in Sevilla, Spain will be held during September 22-26, 1997, see
OP-SF Net 4.2, Topic #4. Updated information can be found on the web page

   http://www.wis.kuleuven.ac.be/wis/applied/walter/sevilla.html

In particular, this contains a link to the conference program on URL

   http://www.wis.kuleuven.ac.be/wis/applied/walter/program.html

Here is the updated list of plenary lectures:

- D. Alpai (Ben Gurion University, Israel): Exact formulas for continuous
     and discrete orthogonal polynomials with rational weights and
     application to solutions of inverse spectral problems
- Alexander I. Aptekarev (Russian Academy of Sciences, Russia):
     Asymptotics of general multiple orthogonal polynomials
- Richard Askey (University of Wisconsin, U.S.A.): Combinatorics of the
     classical orthogonal polynomials
- Tom H. Koornwinder (University of Amsterdam, The Netherlands): A survey
     of symbolic computation for orthogonal polynomials and special
     functions
- Doron Lubinsky (University of Witwatersrand, South Africa): Orthogonal
     polynomials for exponential weights
- Andrei Martinez (University of Almeria, Spain): Asymptotic properties
     of Sobolev orthogonal polynomials
- Paul Nevai (Ohio State University, U.S.A.): Steklov's conjecture in
     L^p and divergence of Lagrange interpolation in L^p
- Evgeni A. Rakhmanov (University of South Florida, U.S.A.): Constrained
     equilibrium measure and zero asymptotics of discrete orthogonal
     polynomials
- Edward B. Saff (University of South Florida, U.S.A.): Theory and
     applications of constrained energ problems
- Herbert Stahl (Technische Fachhochschule Berlin, Germany): Spurious
     poles of Pade approximants
- Vilmos Totik (Bolyai Institute Szeged, Hungary): Orthogonal polynomials
     with respect to varying weights and the so-called universality law



Topic #5   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Meeting on Symmetries and Integrability of Difference Equations

                         FIRST ANNOUNCEMENT

                              SIDE III

            3rd International Interdisciplinary Meeting on
         Symmetries and Integrability of Difference Equations

             SABAUDIA, near Rome (Italy), 16-22 May 1998

        This series of international meetings started in 1994: the first
"Symmetries and Integrability of Difference Equations"  (SIDE) meeting was
held in Esterel, Quebec (near Montreal - Canada) and was organized under
the auspices of the CRM (Centre de Recherches Mathematiques) of the
Universite' de Montreal.  A second meeting took place in 1996 at the
University of Kent in Canterbury (UK). Informations on the 1st SIDE
meeting has been reported in:  "Symmetries and Integrability of Difference
Equations", edited by D. Levi, L. Vinet and P. Winternitz, AMS 1996.

        The meeting is intended to bring together specialists from various
disciplines, all working or using methods from discrete integrable
systems, i.e. systems that can be described by ordinary or partial
difference equations and that allow for exact methods for their solutions.
This domain forms the core of a great variety of fields, including
classical and quantum physics, computer science, mathematical biology,
economics, numerical analysis, difference geometry, and so on.

        The SIDE meetings want to be a point of contact between
researchers of various disciplines on discrete systems which otherwise
would not be able to interact among themselves. The participation of young
scientists is encouraged.  The main topics of the present meeting will be:
integrable difference equations, Symmetries of ordinary and partial
difference equations and reduction techniques, Integrable correspondences,
asymptotics and difference monodromy problems, orthogonal polynomials and
q - special functions, discrete geometry, applications to computer
science, neural network, physical, biological, and economical systems.

        As in the previous meetings of the series, to enhance the
interactions and to promote informal contacts, all the participants will
be accomodated under the same roof, that in this case will be the Hotel
"Oasi di Kufra", as the venue where the lectures are delivered and where
the social activities are organized (meals, receptions, etc.).  So as not
to overload the meeting with talks, while keeping the single-session
format, we plan to accept a limited number of participants (< 50). The
format of the meeting consists of a certain number of short lectures (30
minutes) and of a few longer review expositions intended for students and
young researchers. A poster session will be available for presenting
partial or side results.

        The cost of participation will consist of a registration fee of
Lit. 150000 (equivalent to ~ 90 USD) if paid before March 15th, 1998,
otherwise Lit. 180000 (~ 110 USD) and of a flat all-inclusive rate of
Lit. 810000 (~ 480 USD) ( + Lit. 180000 for single occupancy rooms).  This
flat rate might be partly or completely waived for qualified participants
who have no funds to support their participation if our applications for
financial support will be successful.  The listed prices are subject to
small variations according to fluctuations of the exchange rates.

        Interested persons should contact the local organizers, preferably
by e-mail. Please take into account that there will be room for, at most,
20 talks (30 minutes). Consequently the scientific committee will decide
whether the applicant's contribution can be accepted as a talk or as a
poster.

The following speakers have already confirmed their participation:

C. Brezinski (U. Lille - France) - "Difference equations and convergence
        acceleration methods"
P. Clarkson (U. Kent - UK) -  "Exact solutions of discrete Painleve'
        equations"
V. Enolsky  (U. Kiev - Ukraine) - "Addition laws on hyperelliptic
        Jacobian and integration of discrete systems of KdV type"
F.A. Grunbaum  (U. California, Berkeley - USA) - to be announced
R. Hirota  (Waseda U. - Japan) - "Discretization of integrable systems"
M. Ismail (Univ. of South Florida - USA) - "Asymptotics of recursion
         coefficients and zeros of orthogonal polynomials"
I. Krichever (Columbia U. - USA)  - to be announced
T. Miwa  (RIMS Kyoto - Japan) - "Quantum Knizhnik - Zamolodchikov
         equation and its applications to integrable systems"
L. Nieto (U. Valladolid - Spain) - to be announced
R. Quispel (Latrobe U., Melbourne - Australia) - "Symmetries and
         integrability of difference equations"
A. Ramani  (CNRS - France) - to be announced
G. Rollet (U. Paris Cergy - France) - to be announced
P. Santini  (U. Catania - Italy) - "Discrete geometry and integrable
         difference equations"
J. Satsuma (U. Tokyo - Japan) -"Nonautonomous soliton equations and their
         solutions"
W. Schief (UNSW, Sydney - Australia) - "The geometry of discrete
         integrable systems"
V. Spiridonov (Dubna - Russia) - "Self-similar potentials and q-special
         functions"
Yu. Suris (U. Bremen - Germany) - "Nonlocal quadratic Poisson algebras
         and constrained lattice KP"
M. Tarlini (U. Firenze - Italy) - "Induced representations of the Quantum
         Galilei group and integrable models in 1 space dimension"
W. Van Assche  (U. Louvain - Belgium) - "Non-symmetric linear difference
         equations for polyorthogonal polynomials"
A.P. Veselov (U. Loughborough - UK) - "Laplace - Darboux lattices and
         spectral theory of Schroedinger operators"
L. Vinet (CRM - Canada) - "Algebraic treatment of integrable difference
         equations and special functions"
R. Yamilov (Ufa -Russia) - "Formal symmetry approach to the
         classification and testing of integrable differential difference
         equations"

The local organizers are:
D. Levi, O. Ragnisco (Dipartimento di Fisica, Universita' di Roma Tre -
Via della Vasca Navale 84, 00146 Roma, Italy)
e-mail: levi@amaldi.fis.uniroma3.it, ragnisco@amaldi.fis.uniroma3.it
fax:    39-6-5579303
www:  http://www.roma1.infn.it/~ragnisco/side/sideiii.htm
(Editor's note: As of September 13, 1997, this web site had not been
activated.)

The International Scientific Committee is:
F.W. Nijhoff (U. Leeds - UK) chairman, A. Bobenko (TU Berlin - Germany),
J. Hietarinta (U. Turku - Finland), N. Joshi (U. Adelaide - Australia),
M. Kruskal (Rutgers U. - USA), D. Levi (U. Roma 3 - Italy),
V. Papageourgiou (U.  Patras - Greece), C. Viallet (U. Paris VI - France),
P. Winternitz (U. Montreal - Canada)



Topic #6   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Dan Lozier <lozier@cam.nist.gov>
Subject: NIST Digital Library of Mathematical Functions

A major new World Wide Web site for special functions and their
applications is being planned at the National Institute of Standards and
Technology, provided adequate financial and other resources are secured.
The new site will be called the NIST Digital Library of Mathematical
Functions.  See

     http://math.nist.gov/DigitalMathLib

for current information about the project.

NIST is the new name for the old National Bureau of Standards, and the
core component of the DLMF will be a thorough revision of Abramowitz and
Stegun, Handbook of Mathematical Functions (with Formulas, Graphs, and
Mathematical Tables), NBS Applied Mathematics Series 55, US Government
Printing Office, 1964.  The procedures used to generate and validate the
original handbook will be adapted and strengthened to ensure a successor
of the highest possible quality.

The static content of the DLMF will be stored in a computer database at
NIST, accessible at the web site and by CD-ROM.  The ability will be
provided to copy formulas, graphs and numerical data into local computer
files in formats appropriate for subsequent word, numerical, symbolic and
graphical processing.

Application components in technical fields where special functions are
important are a prominent part of the DLMF concept.  For example, such a
component could include sample problems and their solutions in terms of
special functions.  Basic mathematical information resident in the core
component will be extracted and adapted to the notation and definitional
conventions of the technical field.  Components for electromagnetism and
quantum physics are included in the NIST plan as prototypes for other
application components.

A later stage of development is envisioned in which computational
services are provided by NIST on request from web users.  For example, a
user would be able to specify a set of numerical values for the arguments
and parameters of a special function, together with a minimum precision
requirement.  If the requisite computational resources are available
to the DLMF, then the corresponding set of function values would be
computed and delivered to the user.  Other potential services-on-demand
are preparation of graphs and computer algebraic processing.

Recent events include:

-    The DLMF initiative was presented on July 14 at the
     SIAM Annual Meeting in the OPSF-sponsored Minisymposium
     on Handbooks for Special Functions and the  World  Wide
     Web. A corresponding NIST report will be available
     soon at the web site.

-    A workshop was held July 28-30 at NIST  to refine and
     develop the DLMF concept.  About a third of the 30 participants
     were prominent researchers invited from outside NIST.
     In addition to lectures, lively and useful discussions took
     place on several general topics: approach to the project,
     organization of the project, funding possibilities, new chapter
     layout, roles and applications, and future phases.  A summary NIST
     report will be available soon at the web site.

The web site gives an e-mail address where comments can be sent on any
aspect of the project.  Also, any site visitor can subscribe to a mailing
list to receive occasional e-mail from NIST announcing significant new
developments.

Dan Lozier
(U.S.) National Institute of Standards and Technology



Topic #7   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Student membership in SIAM

The following information may beof interest to students and postgraduates.

Students can become a member of SIAM for $20/year, with free membership in
one activity group.

Postgraduates, during three consecutive years after receiving their
highest degree, can become members of SIAM for $45/year.

E-mail: join@siam.org



Topic #8   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Wolfram Koepf <koepf@zib.de>
Subject: Updated booklist

A combined booklist and list of electronic services appeared in OP-SF NET
2.2, Topic #12. A revised list appeared in our printed Newsletter in June
1997. An electronic version of the revised may be seen at our website:
http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/booklist.html



Topic #9  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Book on Mehler-Fock type transform

The following announcement was found on the web site:
http://www.awl-he.com/advmaths/titles/367.html

   Pitman Research Notes in Mathematics Series 367
   Integral Expansions Related to Mehler-Fock Type Transforms

   B N Mandal and Nanigopal Mandal

   An important class of integral expansions generated by Sturm-Liouville
   theory involving spherical harmonics are commonly known as Mehler-Fock
   integral transforms. In the inverse transformation formulae, the
   subscript of the associated Legendre functions generally appears as the
   integration variable while the superscript is either zero or an integer
   or a complex number. There is another class of integral transforms
   involving associated Legendre functions for which the superscript
   appears as the integration variable in the inverse transformation
   formulae while the subscript remains fixed. This class of integral
   transforms and the associated integral expansions are not widely known
   in the literature and they are somewhat related to Mehler-Fock type
   transforms. In this book, a number of integral expansions of such type
   have been established rigorously and integral expansions of some simple
   functions are also obtained as applications. It is hoped that this book
   will motivate researchers in applied mathematics to initiate work on
   appropriate physical problems in continuum mechanics and
   electromagnetic wave diffraction involving conical, toroidal, and
   ellipsoidal regions.

   Readership: Researchers and graduate students in applied mathematics
   and engineering, engineers and physicists working in electromagnetic
   diffraction problems and elasticity problems.

   Contents:

      * Preface
      * 1. Introduction
      * 2. Integral expansions related to Mehler-Fock transforms
      * 3. Integral expansions related to Mehler-Fock type transforms
        involving associated Legendre functions
      * 4. Integral expansions related to Mehler-Fock type transforms
        involving generalized associated Legendre functions
      * 5. Some further integral expansions
      * Bibliography

   Pages: 144

   AMS: 44
   Subject Classification: Approximation theory, integral transforms and
   integral equations, Mechanics of solids, Mathematical physics
   Publication Year: 1997
   ISBN: 0 582 30816 X



Topic #10  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Proceedings of the Organic Mathematics Workshop

Information on this publication is available at:
http://www.cecm.sfu.ca/organics/contents.html

>From the mission statement:

The Organic Mathematics Project (OMP) is directed towards the
exploration of the emerging network and information technologies
within the context of mathematics.  The end product will be a digital
proceedings of the Workshop on Organic Mathematics on December 12 to
14, 1995 at Simon Fraser University.

See as an example the invited article
"Pfaff's Method (III): Comparison With the WZ Method" by George Andrews.



Topic #11  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Rivlin Festschrift

Annals of Numerical Mathematics Vol 4, 1997 is a special issue on "The
heritage of P.L. Chebyshev: A Festschrift in honor of the 70th birthday of
T.J. Rivlin".  This special issue is edited by Charles A. Micchelli.  The
following table of contents is found at the URL:
http://www.baltzer.nl/anuma/an4-97.html .
A considerable part of the included papers deals with orthogonal
polynomials.

Dedication
Charles A. Micchelli

On the work of Theodore J. Rivlin
C.A. Micchelli

A brief preface
T.J. Rivlin

On Chebyshev polynomials in dynamics
R. Adler, B. Kitchens, C.A. Micchelli and C. Tresser 1

Renewal sequences and ordered partitions
J.M. Anderson and A. Hinkkanen 11

Bounds for the trace of the inverse and the determinant of symmetric
positive definite matrices
Z. Bai and G.H. Golub 29

On approximation by exponentials
B.J.C. Baxter and A. Iserles 39

A discrepancy lemma for oscillating polynomials and sign changes of the
error function of best approximants
H.-P. Blatt 55

On the zeros of various kinds of orthogonal polynomials
C. Brezinski and M. Redivo-Zaglia 67

On the lower semicontinuity of best rational Chebyshev approximation
B. Brosowski 79

Rivlin's problem
B. Brosowski and F. Deutsch 95

Lebesgue functions for polynomial interpolation -- a survey
L. Brutman 111

On a recovery problem
M. Buhmann and A. Pinkus 129

The approximate sampling theorem, Poisson's sum formula, a decomposition
theorem for Parseval's equation and their interconnections
P.L. Butzer and A. Gessinger 143

Support and foundation of bases
J.M. Carnicer, T.N.T. Goodman and J.M. Pen¬a 161

Lacunary interpolation by cosine polynomials
A.S. Cavaretta, C.R. Selvaraj and A. Sharma 181

A study of asymptotically optimal time-frequency localization by scaling
functions and wavelets
C.K. Chui and J.Z. Wang 193
A de Montessus theorem for multivariate homogeneous Padé approximants
A. Cuyt and D.S. Lubinsky 217

The multiplicity of a spline zero
C. de Boor 229

Overconvergence of some simultaneous Hermite-Padé interpolants
M.G. de Bruin and A. Sharma 239

Approximation by feed-forward neural networks
R.A. DeVore, K.I. Oskolkov and P.P. Petrushev 261

Uniqueness of least-norm generalized monosplines induced by log-concave
weight-functions
N. Dyn 289

On upper bounds for the number of extrema of Chebyshev alternants
M.K. El-Daou and E.L. Ortiz 301

Polynomial approximation of functions continuous on [-1, 1] and analytic
on (-1, 1)
D. Gaier 315

On the computation of special Sobolev-type orthogonal polynomials
W. Gautschi 329

On some recursive triangular systems
W.M.Y. Goh, E. Schmutz and J. Wimp 343

On a measure of dissimilarity between positive definite matrices
A.J. Hoffman and C.A. Micchelli 351

On computing Ax and pi^T A, when A is sparse
A.J. Hoffman, W.R. Pulleyblank and J.A. Tomlin 359

The dynamics of group automorphisms
B. Kitchens 369

A variational approach to optimizing linear functionals over Haar spaces
A. Kroo and D. Schmidt 393

Weighted polynomial approximation of some entire functions on the real
line
A. Kroo, J. Szabados and R.S. Varga 405

On monotone and convex approximation by splines with free knots
D. Leviatan and A. Shadrin 415

On optimal Pade-type cuts
A.P. Magnus 435

Subdivision schemes with non-negative masks converge always -- unless they
obviously cannot?
A.A. Melkman 451

On a measure of dissimilarity for normal probability densities
C.A. Micchelli 461

A splitting problem
D.J. Newman 479

Fast multipoint polynomial evaluation and interpolation via computations
with structured matrices
V.Y. Pan, A. Zheng, X. Huang and Y. Yu 483

Bernstein polynomials based on the q-integers
G.M. Phillips 511

A new iterative algorithm for thin plate spline interpolation in two
dimensions
M.J.D. Powell 519

The Fundamental Theorem of Linear Programming applied to certain extremal
problems for polynomials
M.A. Qazi and Q.I. Rahman 529

Optimal recovery in translation-invariant spaces of functions
R. Schaback 547

The Chebyshev constant of a linear set
H.S. Shapiro 557

On the zeros of generalized Jacobi polynomials
P. Vertesi 561

Smoothing spline ANOVA fits for very large, nearly regular data sets, with
application to historical global climate data
G. Wahba and Z. Luo 579

Measurable entire functions
B. Weiss 599

Strong tractability of weighted tensor products
H. Wozniakowski 607

Summability of certain product ultraspherical orthogonal series in several
variables
Y. Xu 623

Author index 639



Topic #12  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Book on Logarithmic Potentials with External Fields

The following information is taken from the web site:
http://www.springer.de/catalog/html-files/deutsch/math/toc/3540570780-c.html

      E. Saff, University of South Florida, Tampa, FL, USA ; V. Totik ,
      University of Szeged, Hungary

      Logarithmic Potentials with External Fields

           This treatment of potential theory emphasizes the effects
           of an external field (or weight) on the minimum energy
           problem. Several important aspects of the external field
           problem (and its extension to signed measures) justify its
           special attention. The most striking is that it provides a
           unified approach to seemingly different problems in
           constructive analysis. These include the asymptotic
           analysis of orthogonal polynomials, the limited behavior
           of weighted Fekete points; the existence and construction
           of fast decreasing polynomials; the numerical conformal
           mapping of simply and doubly connected domains;
           generalization of the Weierstrass approximation theorem to
           varying weights; and the determination of convergence
           rates for best approximating rational functions.

           Potential theory, mathematical physics. For graduate
           students and researchers in the above fields.

      Table of Contents

      1997 . VIII, 525 pp., Hardcover ISBN 3-540-57078-0
      DM 158,-

      Publication date: September, 1997
      Springer, Grundlehren der mathematischen Wissenschaften. Vol. 316



Topic #13  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Maple procedure rec2ortho

Rene' Swarttouw and I have completed a major update of our Maple procedure
rec2ortho (get OP families in the Askey scheme from the coefficients in
the three term recurrence relation).  See more information at the URL:

http://turing.wins.uva.nl/~thk/rec2ortho.html

Tom Koornwinder



Topic #14  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Vadim Zelenkov <zelenkov@gray.isir.minsk.by>
Subject: Krawtchouk Polynomials Home Page

In the near future I intend to create a web site, devoted to the
Krawtchouk orthogonal polynomials. Besides M. Krawtchouk's biography and
the polynomial properties I would like to include references to papers in
which these polynomials are investigated or used.

If you want your article to be mentioned please e-mail me the
bibliographic data, abstract and (if possible) the text in LaTeX format
and/or the appropriate hyperlink.

I shall inform you when the site will be completed.

Thank you in advance,

Vadim Zelenkov,
International Sakharov Institute of Radioecology,
Minsk, Belarus
Email: zelenkov@gray.isir.minsk.by
WWW: http://www.isir.minsk.by/~zelenkov



Topic #15  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW Pages, etc.

Arno Kuijlaars (Leuven, Belgium) is staying temporarily at:

Department of Mathematics
City University of Hong Kong
83 Tat Chee Avenue
Kowloon, Hong Kong
email: maarno@math.cityu.edu.hk

>From February 1, 1998 his address will be again:

Departement Wiskunde
Katholieke Universiteit Leuven
Celestijnenlaan 200 B
3001 Leuven
Belgium
email: arno@wis.kuleuven.ac.be



Topic #16  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Obtaining back issues of OP-SF Net and submitting contributions
         to OP-SF Net and Newsletter

Back issues of OP-SF Net can be obtained from
     ftp:     ftp.wins.uva.nl, in directory
               pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or   WWW:     http://turing.wins.uva.nl/~thk/opsfnet/

or   WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html

Contributions to the OP-SF Net 4.6 should reach the email address
poly@siam.org before November 1, 1997.

The Activity Group also sponsors a (printed) Newsletter edited by Wolfram
Koepf. Deadline for submissions to be included in the October 1997 issue
is September 15, 1997 and for submissions to be included in the
February 1998 issue it is January 15, 1998.

Please send your Newsletter contributions directly to the Editor:

Wolfram Koepf
Konrad-Zuse-Zentrum
Takustr. 7
D-14195 Berlin-Dahlem, Germany
tel.: +49-30-841 85-348/347
fax:  +49-30-841 85-269/125
email: koepf@zib.de

preferably by email, and in latex format. Other formats are also
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Please note that submissions to the Newsletter (if not containing
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publication in OP-SF Net, and vice versa, unless the writer requests
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Previous issues of the Newsletter, but not the most recent one, can
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    http://www.zib.de/koepf/

or by anonymous ftp at

   ftp.zib.de   in directory   pub/UserHome/Koepf/SIAM

In order to join the SIAM Activity Group on Orthogonal Polynomials
and Special Functions, and thereby receive the Newsletter,
you have to become a member of SIAM. The annual dues are $93 for
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