[Fwd: OP-SF Net Volume 7 Number 3]
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Subject: OP-SF Net Volume 7 Number 3
Date: Tue, 16 May 2000 12:06:12 -0400 (EDT)
From: mailer@siam.org
May 15, 2000
O P - S F N E T Volume 7, Number 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editor:
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
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o
Today's Topics
1. From the Editor
2. Sixth international Symposium on Orthogonal Polynomials, Special
Functions and their Applications
3. Conference in Honor of Claude Brezinski
4. Krawtchouk Polynomials Home Page
5. Spherical Cap Harmonic Analysis
6. Question on Fourier expansions
7. Scope of SIAM Journal on Mathematical Analysis
8. OP-SF preprints in xxx archive
9. Changes of Address, WWW Pages, etc
10. Subscribing to OP-SF NET
11. Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Calendar of Events:
2000
May 17-20: Symposium on Trends in Approximation Theory,
Nashville, Tennessee, USA 6.5 #4
May 29 - June 9: Special Functions 2000: Current Perspective
and Future Directions, Tempe, Arizona, USA 6.5 #2, 7.1 #3
July 3-7: Alhambra 2000, a Joint Mathematical European-Arabic
Conference 6.4 #7
July 10-14: SIAM Annual Meeting in Puerto Rico including
Minisymposium on Orthogonal Polynomials and
Special Functions - July 13, 10:30 to 12:30 7.2 #3
July 17-22: I Colloquium on Lie Theory and Applications,
Vigo, Spain 6.4 #8
July 19-26: Third World Congress of Nonlinear Analysts,
Catania, Italy (including session on
"Adaptive quadrature and cubature formulae". 7.1 #6
July 24-28: Summer School "Orthogonal Polynomials and Special
Functions", Laredo, Spain. 6.6 #3
August 5-8: International Symposium on Analysis, Combinatorics
and Computing, Dalian, China 7.1 #7
August 14-18: International Symposium on Applied Mathematics,
Dalian, China 6.5 #5
September 22-28: International Conference on Functional Analysis
and Approximation Theory, Acquafredda di
Maratea, Italy 7.2 #6
November 27 - December 1: 4th International Interdisciplinary
meeting on "Symmetries and Integrability of Difference
Equations", Tokyo, Japan.
Contact persons:
J. Stasuma (satsuma@poisson.ms.u-tokyo.ac.jp) or
T. Tokihiro (toki@poisson.ms.u-tokyo.ac.jp)
2001
June 18-22: Symposium on Orthogonal Polynomials, Special Functions and
Applications, Rome, Italy 7.3 #2
August 20-24: 3rd International meeting on Approximation
Theory, Dortmund, Germany
Contact: idomat@math.uni-dortmund.de
October 1-5: "Numerical Algorithms", Conference in Honor of Claude
Brezinski, Marrakesh, Morocco 7.3 #3
Future plans:
A conference in honor of Bill Jones' 70 th birthday will be organized
at Mesa State College in Grand Junction, Colorado. This will be
organized in the summer of 2001. The date and title will be announced
later. Contact persons are Catherine Bonan-Hamada (cbonan@mesastate.edu)
and Phil Gustafson (pgustafs@mesastate.edu).
As already mentioned in OP-SF NET 6.5, the next meeting in the series
Fields-Toronto (1995) - CRM-Montreal (1996) - Mount Holyoke (1998) - Hong
Kong (1999) - Arizona (2000) is expected to be held in Amsterdam, in
2002, probably in early summer, to be organized by Tom Koornwinder
(thk@uwa.wins.nl), Nico Temme (nico@cwi.nl) and Erik Koelink
(koelink@twi.tudelft.nl).
Topic #1 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: OP-SF Net Editor <muldoon@yorku.ca>
Subject: From the Editor
As well as information about future events, we aim to publish accounts of all
recent meetings devoted to orthogonal polynomials and related areas. But we need
volunteers to write such reports. This is a call for people to write about the
forthcoming "Special Functions 2000" meeting in Tempe, Arizona and the SIAM
Annual meeting in Rio Grande, Puerto Rico, in July. Please contact me if you
would like to write something about these or other meetings.
I am looking for a replacement editor starting in January 2001. If someone
interested, please let me know. It would be best to have a transition period
when the old and new editors could work together. It is possible also to share
the job between two people.
Topic #2 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: Andrea Laforgia <laforgia@dma.uniroma3.it>
Subject: Sixth international Symposium on Orthogonal Polynomials, Special
Functions and their Applications
SIXTH INTERNATIONAL SYMPOSIUM ON ORTHOGONAL POLYNOMIALS, SPECIAL FUNCTIONS
AND APPLICATIONS - OPSFA
FIRST CIRCULAR
Dear colleagues,
The sixth international Symposium on Orthogonal Polynomials, Special
Functions and their Applications will be held on June 18 - 22, 2001 in
Roma (Italy).
The 6th OPSFA follows the European Conferences of Bar-Le-Duc (France,
1984), Segovia (Spain, 1986), Erice (Italy, 1990), Granada (Spain, 1991,
VII SPOA), Evian (France, 1992), Delft (Holland, 1994, in honour of
Thomas Jan Stieltjes Jr. (1856-1894)), Sevilla (Spain, 1997, VIII SPOA)
and Patra (Greece, 1999, in honour of Theodore Chihara).
The scientific program is currently being elaborated by the scientific
committee: A. Laforgia (Universita` Roma Tre, Italy), P. E. Ricci
(Universita` "La Sapienza", Roma, Italy), M. De Bruin (University of
Delft, Netherlands), F. Marcellan (Universidad Carlos III, Madrid, Spain),
P. D. Siafarikas (University of Patras, Greece), M. Muldoon (York
University, Canada), R. Wong (City University of Hong Kong, China). It
will consist, as usual, of some plenary lectures and short communications
(20 minutes). The second circular, to be distributed in autumn 2000, will
give more information about it.
The cost of attendance is expected to be quite reasonable. The
registration fee will be around 250 Euros, which includes the admission to
the Symposium, a copy of the book of abstracts, a copy of the Proceedings,
reception and participation in some social events (welcome drink, visit to
Rome's surroundings, etc.).
To help us with the organization of the Symposium we would appreciate if,
even at this early stage, you could indicate your potential attendance in
the attached preliminary registration form. If you are interested in being
invited to participate or in receiving subsequent circulars, please fill
out the preregistration form and return it not later than May 31, 2000 to
the Symposium mailing address.
More details about accommodation, travelling expenses and transportation
of the participants from the airport will be given in the next circulars.
Mailing address:
Sixth International Symposium on Orthogonal Polynomials, Special
Functions and their Applications.
Dipartimento di Matematica (to prof. Andrea LAFORGIA)
Universita` Roma Tre
Largo S. Leonardo Murialdo, 1
00146 ROMA (Italy)
tel. +39+06+54888025, 54888008; fax 54888072.
NOTICE: You may also send the preregistration form via e-mail; please see
the Web page www.mat.uniroma3.it/opsfa2001. You may also use the e-mail
address of the Symposium opsfa2001@mat.uniroma3.it or the e-mail addresses
of the members of the local organizing committee:
prof. Andrea LAFORGIA: laforgia@mat.uniroma3.it
prof. Paolo Emilio RICCI: riccip@.uniroma1.it
dott. Pierpaolo NATALINI: natalini@mat.uniroma3.it
dott.ssa Silvia NOSCHESE: noschese@uniroma1.it
dott. Biagio PALUMBO: palumbo@mat.uniroma3.it
Please bring this announcement to the attention of interested people.
Looking forward to seeing you in Roma
Cordially yours,
Andrea LAFORGIA
(on behalf of the Organizing Committee)
SIXTH INTERNATIONAL SYMPOSIUM
ON ORTHOGONAL POLYNOMIALS,
SPECIAL FUNCTIONS AND APPLICATIONS
ROMA, June 18 - 22, 2001
PREREGISTRATION FORM
Please answer soon to help us to plan the Symposium
NAME __________________________________________________________________
INSTITUTION ____________________________________________________________
ADDRESS _______________________________________________________________
TELEPHONE _________________________ FAX ______________________________
E-MAIL ADDRESS ________________________________________________________
( ) I am interested in attending the Symposium
( ) My plans are uncertain, but I would like to receive subsequent
circulars
( ) I would like to give a 20 minute communication
(tentative title: _____________________________________________________)
( ) I would like to bring a companion
Please return this form not later than May 31, 2000 to the Symposium
Address:
SIXTH INTERNATIONAL SYMPOSIUM ON ORTHOGONAL POLYNOMIALS, SPECIAL
FUNCTIONS AND THEIR APPLICATIONS
Dipartimento di Matematica
Universita` di Roma Tre
Largo S. Leonardo Murialdo, 1
00146 ROMA (Italy)
Local organizing committee
A. Laforgia, P. E. Ricci, P. Natalini, S. Noschese, B. Palumbo, F.
Pascucci
tel. +39+06+54888025, 54888008; fax 54888072.
E-mail: opsfa2001@mat.uniroma3.it
Web Page: http://web.mat.uniroma3.it/opsfa2001/
Topic #3 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Conference in Honor of Claude Brezinski
Preliminary announcement
International Conference on
"NUMERICAL ALGORITHMS"
dedicated to
CLAUDE BREZINSKI
on the occasion of his 60th birthday
Marrakesh, Morocco
October 1-5, 2001
We intend to organize an international conference in October 2001 to
celebrate the 60th birthday of Claude Brezinski and, at the same time, the
10th anniversary of the journal Numerical Algorithms that he founded in
1991 and where contributed papers will be published. The themes of the
conference will cover all aspects of Numerical Analysis, in particular
those which are related to numerical algorithms. The goal of this
conference is to bring together experts from these areas. The numerical
analysis community is warmly invited to attend so that we have a valuable
scientific meeting and celebrate Claude's 60th birthday at the banquet.
Participants will be accommodated in a 4-star hotel, comparable to the best
European or American hotels, at a special reduced price. In Marrakesh, the
weather is very nice in October and the town can be easily reached by
plane from Casablanca (one hour). Casablanca has direct connections to
major European cities and to New York and Montreal.
A web site containing all the informations about this conference can be
found at
http://www-lma.univ-littoral.fr/~na2001
If you are interested in participating, please notify us as soon as possible
at the address
na2001@lma.univ-littoral.fr
In this way, you will regularly receive new updated informations about this
event.
Organizing committee:
B. Beckermann (University of Lille I, France)
A. Bentbib (Faculty of Sciences and Technologies, Marrakesh, Morocco)
B. Germain-Bonne (University of Lille I, France)
J.-P. Chehab (University of Lille I, France)
M. El Alaoui-Talibi (Faculty of Sciences Semlalia, Marrakesh, Morocco)
A. Fdil (ENS, Marrakesh, Morocco)
A. Lembarki (Faculty of Sciences Semlalia, Marrakesh, Morocco)
M. Prevost (University of Littoral, Calais, France)
A. Matos (University of Lille I, France)
A. Messaoudi (ENS, Rabat, Morocco)
M. Redivo-Zaglia (University of Calabria, Cosenza, Italy)
R. Sadaka (ENS, Rabat, Morocco)
H. Sadok (University of Littoral, Calais, France)
J. Van Iseghem (University of Lille I, France)
Topic #4 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: Vadim Zelenkov <zelenkov@isir.minsk.by>
Subject: Krawtchouk Polynomials Home Page
After a long pause I have updated the Krawtchouk Polynomials Home Page at:
http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn/
What is new?
11 references added to the Bibliography.
How to spell: Krawtchouk or Kravchuk? Please express your opinion (I would
like to complete the voting before the next Krawtchouk/Kravchuk conference
which will take place in May).
Search facilities.
Full text of the article (1929) in which Krawtchouk polynomials were
introduced (in French original, English and Russian translations). If
anybody could help to translate the text also into Ukrainian - it could be
"in resonance" with Krawtchouk's ideas!
Important: if you cannot read the text of the article which have been
converted from LaTeX to HTML by TTH please let me know what operating
system you use.
So welcome to http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn/
Topic #5 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: William M. Robertson <wmrobert@ix.netcom.com>
Subject: Spherical Cap Harmonic Analysis
I would like to draw my colleagues' attention to several recent papers
and two older papers on Spherical Cap Harmonic Analysis and its
application to gravity and magnetism, which appeared in journals which
OP-SF colleagues may not be usually reading.
Spherical Cap Harmonic Analysis involves functions which are orthogonal
over a spherical cap (a circular region on the sphere), namely the
Associated Legendre Functions of NON-integer degree but integer order,
multiplied by the usual cosine and sine multiple-angle functions.
These papers are (in reverse chronological order):
* A. De Santis and J.M. Torta, "Spherical cap harmonic analysis: a
comment on its proper use for local gravity field representation", Journal
of Geodesy, 71, 526-532, (1997). [The Journal of Geodesy is the merger and
continuation of the Bulletin Geodesique and the manuscripta geodaetica
journals].
* C-W Hwang and S-K Chen, "Fully normalized spherical cap harmonics:
applications to the analysis of sea-level data from TOPEX/POSEIDON and
ERS-1", Geophysical Journal International, 129(2) 450-460, (1997).
* Li Jiancheng, Chao Dingbo, and Ning Jinsheng, "Spherical cap harmonic
expansion of local gravity field representation", manuscripta
geodaetica, 20(4), 265-277, (1995).
* G.V. Haines, "Computer Programs for Spherical Cap Harmonic Analysis
of Potential and General Fields", Computers and Geosciences, 14(4),
413-447, (1988).
* G.V. Haines, "Spherical Cap Harmonic Analysis", Journal of
Geophysical Research, 90(B3), 2583-2591, (28 Feb 1985).
Topic #6 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: Nikolai Nikolaev <nikolaev@nws.aubg.bg>
Subject: Question on Fourier expansions
Could somebody please tell me where can I read more about the Fourier expansion
with NON-multiple frequencies, like:
f(t) = Sum[ A*sin(wt)+B*cos(wt) ] where: w = 2*pi/T+k
which is different from the case with multiple frequencies w = ( 2*pi*k) / T used
to describe periodic signals.
Thank you very much for the attention!
Nikolay Nikolaev
Assistant Professor of Computer Science
American University of Bulgaria
www.aubg.bg/nws/~nikolaev/
Topic #7 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: Daniel Lozier <dlozier@nist.gov>
Subject: Scope of SIAM Journal on Mathematical Analysis
The Officers of our Activity Group have submitted the following statement
to Jim Crowley and Gil Strang (SIAM executive director and president,
respectively). The executive Director intends to share this information
with the new Editor-in-Chief of SIAM Journal on Mathematical Analysis.
STATEMENT BY THE OFFICERS OF SIAM SIAG-OPSF ON THE SCOPE OF SIMA
D. Lozier, Chair
W. Van Assche, Vice-Chair
C. Dunkl, Secretary
F. Marcellan, Program Director
The SIAM Journal on Mathematical Analysis (SIMA) was traditionally one of
the better journals for publishing papers dealing with special functions.
Until volume 19 (number 6, 1988), the scope of the journal was:
"Contains research articles on those parts of mathematical analysis that
grow from and are applicable to engineering, the natural sciences, and
numerical analysis. Topics include partial differential equations,
functional analysis, bifurcation theory, dynamical systems, differential
geometry, asymptotic analysis, harmonic analysis, integral transforms, and
special functions."
In this list, the topics "asymptotic analysis, harmonic analysis, integral
transforms, and special functions" indeed deal with aspects which are of
interest to the SIAM Activity Group on Orthogonal Polynomials and Special
Functions, which was founded in 1990.
It can be said that special functions are to mathematics the way
mathematics is to the natural sciences; they are key tools. Consider
important appearances in recent research areas: completely integrable
quantum models, algebraic combinatorics, number theory, asymptotics, group
representations, Fourier transforms, tomography, quantum groups, DeBranges
proof of the Bieberbach conjecture, etc. In fact, the importance of
special functions is demonstrated conclusively in the past 25 years of
data from the Science Citation Index for Abramowitz & Stegun's Handbook of
Mathematical Functions. Not only has the absolute number of citations of
Abramowitz and Stegun been increasing steadily, its rate of growth exceeds
the growth rate for the Index as a whole.
Unfortunately, starting from volume 20 (number 1, 1989), the scope of SIMA
was changed and the topics mentioned earlier disappeared from the scope.
Now the papers in the journal fall into two broad categories, the first
being those that analyze interesting problems associated with realistic
models for natural phenomena. The second category includes those papers
which contribute in a substantial way to the general, analytical
information and techniques which are likely to bear upon such models.
Thus the journal no longer reflects as strongly as before the interest of
our SIAG. Furthermore, no one on the present editorial board represents
the research topics of interest to our SIAG. This was certainly different
in the past, when F.W.J. Olver, R. Askey, G. Andrews and others were on
the editorial board. Volume 25 (number 2, 1994) was an important special
issue dedicated to Askey and Olver that contained several important papers
which proved to be relevant to our SIAG. It is a pity that since then
only few papers dealing with special functions were published in SIMA.
Our activity group strongly urges that the scope of the SIAM Journal on
Mathematical Analysis again include such topics as special functions and
rigorous asymptotics, and put more emphasis on mathematical analysis than
on applied mathematics. After all, SIAM also publishes the SIAM Journal
on Applied Mathematics for which the scope has a large intersection with
the present scope of SIMA. The editorial board should have some members
capable of judging papers on orthogonal polynomials and special functions.
The SIAG is willing to advise in this matter.
Topic #8 ------------ OP-SF NET 7.3 ------------- May 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor <muldoon@yorku.ca>
Subject: OP-SF preprints in xxx archive
The following preprints related to the field of orthogonal
polynomials and special functions were recently posted or cross-listed to
one of the subcategories of the xxx archives. See:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
math.CA/0004053
Title: The Askey-Wilson function transform
Author: Erik Koelink, Jasper V. Stokman
Categories: CA Classical Analysis (QA Quantum Algebra; RT Representation Theory)
Math Subject Class: 33D45, 44A20, 33D80, 44A60
Comments: LaTeX2e file. 19 pages
Abstract: In this paper we present an explicit (rank one) function transform
which contains several Jacobi-type function transforms and Hankel-type
transforms as degenerate cases. The kernel of the transform, which is given
explicitly in terms of basic hypergeometric series, thus generalizes the
Jacobi function as well as the Bessel function. The kernel is named the
Askey-Wilson function, since it provides an analytical continuation of the
Askey-Wilson polynomial in its degree. In this paper we establish the
$L^2$-theory of the Askey-Wilson function transform, and we explicitly
determine its inversion formula.
From: Jasper V. Stokman <jstokman@wins.uva.nl>
Date: Mon, 10 Apr 2000 12:16:43 GMT (18kb)
math.CA/0004001
Title: An asymptotic expansion for a ratio of products of gamma functions
Author: Wolfgang Buehring
Categories: CA Classical Analysis
Math Subject Class: 33B15
Comments: 8 pages
Abstract: An asymptotic expansion of a ratio of products of gamma functions
is derived. It generalizes a formula which was stated by Dingle, first proved
by Paris, and recently reconsidered by Olver.
From: Wolfgang Buehring <buehring@rho0.physi.uni-heidelberg.de>
Date: Sat, 1 Apr 2000 10:42:29 GMT (4kb)
math.CO/0005008
Title: On the Asymptotics of Takeuchi Numbers
Author: Thomas Prellberg
Categories: CO Combinatorics (CA Classical Analysis)
Math Subject Class: 05A16
Comments: latex file with 13 pages, 2 postscript figures included
Abstract: I present an asymptotic formula for the Takeuchi numbers $T_n$. In
particular, I give compelling numerical evidence and present a heuristic
argument showing that $$T_n\sim C_T B_n\exp{1\over2}{W(n)}^2$$as $n$ tends to
infinity, where $B_n$ are the Bell numbers, W(n) is Lambert's $W$ function,
and $C_T=2.239...$ is a constant. Moreover, I show that the method presented
here can be generalized to derive conjectures for related problems.
From: Thomas Prellberg <tprell@suhep.phy.syr.edu>
Date: Mon, 1 May 2000 16:21:06 GMT (17kb)
hep-th/0004153
Title: Central Binomial Sums, Multiple Clausen Values and Zeta Values
Authors: J. M. Borwein, D. J. Broadhurst, J. Kamnitzer
Categories: (CA Classical Analysis)
Report number: OUT--4102--88, CECM 99:137
Comments: 17 pages, LaTeX, with use of amsmath and amssymb packages, to appear in
Journal of Experimental Mathematics
Abstract: We find and prove relationships between Riemann zeta values and
central binomial sums. We also investigate alternating binomial sums (also
called Apéry sums). The study of non-alternating sums leads to an
investigation of different types of sums which we call multiple Clausen
values. The study of alternating sums leads to a tower of experimental
results involving polylogarithms in the golden ratio. In the non-alternating
case, there is a strong connection to polylogarithms of the sixth root of
unity, encountered in the 3-loop Feynman diagrams of {\tt hep-th/9803091} and
subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and
hep-th/0004010.
From: David Broadhurst <D.Broadhurst@open.ac.uk>
Date: Sat, 22 Apr 2000 14:09:01 GMT (13kb)
math.CA/0003148
Title: Second-order linear differential equations with two irregular singular
points of rank three: the characteristic exponent
Author: Wolfgang Buehring
Categories: CA Classical Analysis
Math Subject Class: 34A20; 34A25; 34A30
Comments: 33 pages
Abstract: For a second-order linear differential equation with two irregular
singular points of rank three, multiple Laplace-type contour integral
solutions are considered. An explicit formula in terms of the Stokes
multipliers is derived for the characteristic exponent of the multiplicative
solutions. The Stokes multipliers are represented by converging series with
terms for which limit formulas as well as more detailed asymptotic expansions
are available. Here certain new, recursively known coefficients enter, which
are closely related to but different from the coefficients of the formal
solutions at one of the irregular singular points of the differential
equation. The coefficients of the formal solutions then appear as finite
sums over subsets of the new coefficients. As a by-product, the leading
exponential terms of the asymptotic behaviour of the late coefficients of the
formal solutions are given, and this is a concrete example of the structural
results obtained by Immink in a more general setting. The formulas displayed
in this paper are not of merely theoretical interest, but they also are
complete in the sense that they could be (and have been) implemented for
computing accurate numerical values of the characteristic exponent, although
the computational load is not small and increases with the rank of the
singular point under consideration.
From: Wolfgang Buehring <buehring@rho0.physi.uni-heidelberg.de>
Date: Fri, 24 Mar 2000 12:23:10 GMT (19kb)
math.CV/0003175
Title: On zeros of polynomials orthogonal over a convex domain
Authors: V. V. Andrievskii, I. E. Pritsker, R. S. Varga
Categories: CV Complex Variables (CA Classical Analysis)
Math Subject Class: 30C10, 30C15, 30C85, 41A10
Comments: 24 pages; to appear in Constr. Approx
Abstract: We establish a discrepancy theorem for signed measures, with a
given positive part, which are supported on an arbitrary convex curve. As a
main application, we obtain a result concerning the distribution of zeros of
polynomials orthogonal on a convex domain.
From: Igor E Pritsker <igor@math.okstate.edu>
Date: Mon, 27 Mar 2000 18:28:43 GMT (15kb)
math-ph/0003005
Title: Discrete phase integral method for five-term recursion relations
Author: Anupam Garg
Categories: MP Mathematical Physics (CA Classical Analysis)
Comments: Revtex; 7 ps figures
Abstract: A formalism is developed to study certain five-term recursion
relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods.
Such recursion relations arise naturally in the study of the Schrodinger
equation for certain spin Hamiltonians. The conditions for the validity of
the phase integral approximation are derived. It is shown that in contrast to
the three-term problem, it is now possible to get a turning points "under the
barrier", i.e., in the classically forbidden region, as well as inside the
classically allowed region. Further, no qualitatively new types of turning
points arise in recursion relations with still higher numbers of terms. The
phase integral approximation breaks down at the new turning points, requiring
new connection formulas, which are derived.
From: Anupam Garg <garg@vidvan.phys.nwu.edu>
Date: Wed, 8 Mar 2000 15:24:51 GMT (32kb)
math.CO/9907183
Title: On Multi-color partitions and the generalized Rogers-Ramanujan identities
Authors: Naihuan Jing, Kailash Misra, Carla Savage
Categories: CO Combinatorics (QA Quantum Algebra)
Comments: Latex2e, corrected version
Abstract: Basil Gordon, in the sixties, and George Andrews, in the seventies,
generalized the Rogers-Ramanujan identities to higher moduli. These
identities arise in many areas of mathematics and mathematical physics. One
of these areas is representation theory of the infinite dimensional Lie
algebra, where various known interpretations of these identities have led to
interesting applications. Motivated by their connections with Lie algebra
representation theory, we give a new interpretation of the product side of
generalized Rogers-Ramanujan identities in terms of multi-color partitions.
From: jing@math.ncsu.edu
Version 1: Thu, 29 Jul 1999 03:09:04 GMT (12kb)
Version 2: Fri, 28 Apr 2000 17:58:52 GMT (15kb)
math.CO/0004019
Title: Une q - spécialisation pour les fonctions symétriques monomiales
Author: Michel Lassalle (CNRS,Paris)
Categories: CO Combinatorics
Comments: 25 pages, LaTeX, in French. Enlarged version, with new remarks,
misprints corrected, and an Appendix added
Abstract: We obtain the specialization of monomial symmetric functions on the
alphabet (a-b)/(1-q). This gives a remarkable algebraic identity, and four
new developments for the Macdonald polynomial associated with a row. The
proofs are given in the framework of $\lambda$-ring theory.
From: Lassalle <lassalle@labri.u-bordeaux.fr>
Version 1: Tue, 4 Apr 2000 20:07:53 GMT (11kb)
Version 2: Thu, 20 Apr 2000 18:41:21 GMT (12kb)
math.CO/0004012
Title: Schur's old determinant proves a brand-new theorem of
Garrett-Ismail-Stanton
Author: Helmut Prodinger
Categories: CO Combinatorics
Math Subject Class: 05A30
Abstract: Garrett, Ismail, and Stanton gave a general formula that contains
the Rogers-Ramanujan identities as special cases. We show how easy this is
when using a determinant that Schur introduced in 1917.
From: Helmut Prodinger <helmut@cam.wits.ac.za>
Date: Mon, 3 Apr 2000 12:40:58 GMT (3kb)
math-ph/0004028
Title: On the use of Mellin transform to a class of q-difference-differential
equations
Author: Choon-Lin Ho (Tamkang University, Taiwan)
Categories: MP Mathematical Physics (QA Quantum Algebra)
Journal reference: Phys. Lett. 268A (2000) 217
Comments: 13 pages, LaTex, no figures
Abstract: We explore the possibility of using the method of classical
integral transforms to solve a class of $q$-difference-differential
equations. The Laplace and the Mellin transform of $q$-derivatives are
derived. The results show that the Mellin transform of the $q$-derivative
resembles most closely the corresponding expression in classical analysis,
and it could therefore be useful in solving certain $q$-difference equations.
From: Choon-Lin Ho <hcl@mail.tku.edu.tw>
Date: Sun, 23 Apr 2000 13:48:06 GMT (7kb)
Topic #9 ------------ OP-SF NET 7.3 ------------- May 15, 2000
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From: OP-SF NET Editor <muldoon@yorku.ca>
Subject: Changes of Address, WWW Pages, etc
Semyon Yakubovich writes that he is now at the University of Porto. His
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Prof. S.Yakubovich
Departamento de Matematica Pura
Faculdade de Ciencias
Universidade do Porto
4099-002 Porto
Portugal
email: yakubov@agc0.fc.up.pt
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