It is well known the increasing attention paid in the last years to
the theory of Orthogonal Polynomials. In particular since their applications
in a lot of different areas like numerical integration, spectral methods,
interpolation, approximation theory, etc. Also in combinatorics, mathematical
physics, quantum physics, etc. For this reason the *Universidad Carlos
III de Madrid* organizes every two years an international workshop devoted
to this topic. The first edition in 1992 was dedicated to Sobolev orthogonal
polynomials, in 1994 to polynomials orthogonal in the unit circle, the
IWOP'96
,
held in 1996, to the applications of orthogonal polynomials in mathematical
physics, IWOP'98 was devoted to the
*numerical applications and symbolic algorithms*, and
and the last one, the 2002's edition
to the Approximation Theory.

The main **aim** of this 2004's edition of the Workshop was that a
reduced number of invited mathematicians discuss and review recent progress
of the Theory of **Orthogonal Polynomials** in **Mathematical Physics**.
The Workshop will take place at the "Sala de Audiovisuales de la Biblioteca"
located in the cellar (basement) of the Library
(building No. 3 in the map
) of the the Escuela Politécnica Superior of the Universidad Carlos III de Madrid,
**Leganés** (Madrid).

For a detailed map of the the campus of Leganes visit WWW (the Library is the building No. 3 in red). The "Sala de Audiovisuales de la Biblioteca" is in the cell ( click here to see a scheme).

The IWOP04 was sponsored by Comunidad de Madrid, Universidad Carlos III de Madrid, Real Sociedad Matemática Española (RSME) and Sociedad Española de Matemática Aplicada.

**The topics considered** were:
Information Entropy, Imaging Theory, Integrable systems,
Special functions, Pade Approximation, Riemann-Hilbert Problem,
Orthogonal Polynomials.

There were 14 plenary lectures and 18 short communications.

**How to get Escuela Politécnica Superior**

The best way to get the Escuela Politécnica Superior is by using
the trains *Cercanias*which
can be reach from Atocha Railway Station
*Cercanias* Line C5 (direction Fuenlabrada) and leave the train in the Station *Leganés* (not
in Zarzaquemada!) which is at 5 min. waking from the University. Also you can use the MetroSur Line 12,
and leave at
San Nicasio or at
Lenanes Central
Please
see a scheme of getting to the University
Campus , or if you prefer, see a more detailed map

- Dr. Natig Atakishiyev (natig@matcuer.unam.mx) Instituto de Fisica y Matematicas, UNAM, Cuernavaca, Mexico "Duality of q-polynomials, orthogonal on an infinite set of discrete points"
- Dr. Peter A. Clarkson (P. A. Clarkson@kent.ac.uk) Institute of Mathematics, Statistics and Actuarial Science, University of Kent, UK "Painleve equations: Rational solutions and associated special polynomials"
- Dr. Atanassios Fokas (T.Fokas@damtp.cam.ac.uk) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK "1. Chebyshev polynomials and the imaging of the brain 2. Orthogonal polynomials and the Riemann-Hilbert problem."
- Dr. F. Alberto Grunbaum (grunbaum@math.berkeley.edu) Department of Mathematics, University of California, Berkeley, USA "Orthogonal polynomials in medical imaging: a two way street"
- Dr. Jesus Sanchez Dehesa (dehesa@ugr.es) Departamento de Fisica Moderna, Universidad de Granada.Spain "Information Theory of Special Functions, Parts I and II"
- Dr. Juan A. Tirao (jatirao@yahoo.com.ar) Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba, Argentina "Spherical functions, hypergeometric equation and orthogonal polynomials, scalar and matrix valued versions, Parts I and II".
- Dr. Alexei.Zhedanov (zhedanov@kinetic.ac.donetsk.ua) Donestk Institute for Physics and Technology, Ukraine "Explicit schemes of the multipoint Pade interpolation and special functions"

- R. Álvarez-Nodarse (Univ de Sevilla)
- J. Arvesú (Univ. Carlos III) (Secretary)
- F. Marcellán (Chairman) (Univ. Carlos III)

**Collaborators of the Organizing Committee (Local Commitee)**:
Jorge Sanchez, Maria Isabel Bueno, Maria Antonia Delgado, Angeles Garrido,
Roberto Costas Santos

- J. S. Dehesa (Univ. de Granada),
- A. Durán (Univ. Sevilla)
- G.López Lagomasino (Univ. Carlos III),
- F. Marcellán (Univ. Carlos III)
- W. Van Assche (Katholieke Univ. Leuven)

The registration fee is 150 Euros to be paid (in cash) in the opening session (Monday July 5, at 8:30). It includes the all lunches and the social events.

It is possible to use the Hotel *Tryp LEGANES*
with an University price for the IWOP04's participants,
but also the participants can contact with the
Sol Meliá Reservation Service in the phone 902 14 44 40, or
on-line in the WWW.
The rooms have remote-controlled satellite TV,
direct-dial telephone, computer connection, air-conditioning, etc.
The interested people should contact via e-mail to
unicarlosiii@viajeseci.es .
Further information about the Hotel
can be found
cliking here. Where is the Hotel?

The registration starts on Monday 5 at 8:45am and the opening sesion will be on Monday 5 at 9:15 am. The schedule will be during the next week (June 14-18).

- Dr. Natig Atakishiyev (natig@matcuer.unam.mx) Instituto de Fisica y Matematicas, UNAM, Cuernavaca, Mexico "Duality of q-polynomials, orthogonal on an infinite set of discrete points"
- Dr. Peter A. Clarkson (P. A. Clarkson@kent.ac.uk) Institute of Mathematics, Statistics and Actuarial Science, University of Kent, UK "Painleve equations: Rational solutions and associated special polynomials"
- Dr. Atanassios Fokas (T.Fokas@damtp.cam.ac.uk) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK "1. Chebyshev polynomials and the imaging of the brain 2. Orthogonal polynomials and the Riemann-Hilbert problem."
- Dr. F. Alberto Grunbaum (grunbaum@math.berkeley.edu) Department of Mathematics, University of California, Berkeley, USA "Orthogonal polynomials in medical imaging: a two way street"
- Dr. Jesus Sanchez Dehesa (dehesa@ugr.es) Departamento de Fisica Moderna, Universidad de Granada.Spain "Information Theory of Special Functions, Parts I and II" Departamento de Fisica Moderna, Universidad de Granada.Spain "Information Theory of Special Functions, Parts I and II"
- Dr. Juan A. Tirao (jatirao@yahoo.com.ar) Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba, Argentina "Spherical functions, hypergeometric equation and orthogonal polynomials, scalar and matrix valued versions, Parts I and II".
- Dr. Alexei.Zhedanov (zhedanov@kinetic.ac.donetsk.ua) Donestk Institute for Physics and Technology, Ukraine "Explicit schemes of the multipoint Pade interpolation and special functions"

1. Systems of orthogonal polynomials defined by hypergeometric type equations by Nicolae Cotfas

2. Entropy of Pollaczek polynomials by A. Martinez-Finkelshtein and J. Sanchez-Lara (*)

3. Bezout polynomials for classical orthogonal polynomials by I. Area, E. Godoy, A. Ronveaux, and A. Zarzo(*)

4. New inequalities from classical Sturm theorems by Alfredo Deaño (*) et al.

5. Vector Functions Orhogonal to the Gradient of Orthogonal Polynomials. Examples and Properties by Eva Acosta (*) y J.L. Quintela

6. Two classical theorems for the infinite Hessenberg matrix D by V. Tomeo(*) and E. Torrano

7. Recurrence relations for continuous and discrete wave functions by Luis Cardoso

8. Asymptotics of Jacobi polynomials orthogonal on a single contour by R. Orive

9. Anomalous semi-classical and q-semi-classical polinomials of class 1 by J.C. Medem

10. Polynomial perturbations of bilinear functionals and Hessenberg matrices by Maribel Bueno

11. Wavelet generators based on classical orthogonal polynomials and functions of the second kind by M. Moncayo (*) & R. J. Yáñez

12. q-Orthogonal Polynomials Related to the Quantum Group Uq(SO(5)) by Alexander Rozenblyum

13. Classical bases expansions for Macdonald polynomials by M. Schlosser

14. Asymptotic Expansions of Gamma(a,z) and gamma(a,z) for a and z large by C. Ferreira, J.L. López and E. Pérez Sinusía (*).

15. Symmetric hierarchy of the fourth Painlev\'e equation by Filipuk G.V. (*) and Clarkson P.A.

16. A One-Dimensional Model Of Diffusion In A Non-Homogeneous Domain by Igor Fedotov, Julian Marais (*) et al.

17. On continued RogersRamanujan's fraction by V.I.Buslaev

18. Approximation of functions on the unit sphere by the orthogonal spherical polynomials by Yuri N. Skiba.

**Titles **

1. Fourier-Padé Approximants for Angelesco Systems by M. Bello
Hernández and J. Mínguez Ceniceros

2. Approximation by summation methods of the Mellin-Fourier series.
Andi Kivinukk

3. The q-Hahn polynomials and the Clebsh-Gordan coefficients for
the q-algebras SUq(2) by J. Arvesu

4. Generalized Weighted Sobolev Spaces and Applications to Sobolev
Orthogonal Polynomials I. by J.M. Rodriguez, V. Alvarez, E. Romera, and
D. Pestana

5. Weierstrass' theorem in weighted sobolev spaces with k derivatives
by A. Portilla, Y. Quintana, J. M. Rodriguez, and E. Touris.

6. Invariance of the stationary Schr\"{o}dinger equation
and Ladder Operators of special and quantum functions by J. Garc\'{\i}a
Ravelo and A. Queijeiro.

7. Information entropy and standard deviation of probability
distributions involving orthogonal polynomials by Julio I. de Vicente
and J. Sanchez Ruiz

8. On exactly solvable quantum models by R. Alvarez Nodarse, J.
Petronilho and N.R. Quintero

9. q-Racah coefficients and q-Racah polynomials for the q-algebras
SUq(2) and SUq(1,1) by R. Alvarez Nodarse, R. Costas-Santos, and Yu. F.
Smirnov.

10. A simplification of the Laplace and Steepest Descents methods by
Chelo Ferreira, José Luis López and Ester Pérez
Sinusía

11. Using Legendre Polynomials and Block-Pulse Functions for Numerical
Solution of Integro-Differential Equation M. Shahrezaee

12. Moment matrix of self similar measures by C. Escribano, M.
Asunción, and E. Torrano

13. The compact representation of a Leonard pair by Paul Terwilliger

14. Another approach to the analysis of stepped structures for the wave
equation by Igor Fedotov, Steve Jouibert, Michael Shatalov and Julian Marais

To get more information please contact with:

J. Arvesú (jarvesu@math.uc3m.es), R. Álvarez-Nodarse (ran@us.es) and F. Marcellán (pacomarc@ing.uc3m.es)

Maintained by Renato Álvarez-Nodarse: E-Mail: ran@us.es