Orthogonal Polynomials and Special Funct ions SIAM Activity Group on Orthogonal Polynomials and Special Functions scscsr3c Newsletter **** Published Three Times a Year June 2002 Volume 12, Number 3 Contents Net and the Newsletter. One of us (RAN) is leaving the editorship activities because he was From the Editors ............................... 1 appointed as an assistant of the General Editor Obituary ...................................... 1 of the Spanish Royal Mathematical Society (Real Reports fram Meetings and Conferences ......... 3 Sociedad Matematica Espaiiola) in February Forthcoming Meetings and Conferences ......... 4 Future Planning ................................ 8 2002. We want to thank all officers for their Books and Journals ............................. 8 help and support during this four years, specially OP-SF Preprints ................................11 Charles Dunkl, Martin Muldoon and Walter Van Problems and Solutions ........................ 16 Assche whose comments helped us to improve the Miscellaneous .................................. 17 About the Activity Group ..................... 18 Newsletter. How to Contribute to the Newsletter ........... 18 Activity Group: Addresses ..................... 19 As usual, we thank all the contributors to the present issue and hope you will find interesting and useful information in the Newsletter. June 15, 2002 Renato ~lvarez-Nodarse (ran@us . es) Rafael J. YGiez (ryanez@ugr . es) Obituary: W.J. Thron (1918-2001) From the Editors Wolfgang Joseph Thron, professor emeritus of This is the new issue for the summer of 2002 mathematics of the University of Colorado in and it will be the last one of the present team Boulder, Colorado, died at home of emphysema on of CO-editors. As it was announced in the pre- August 21, 2001, a few days after his 83rd birth- vious issues a new Communications Committee day. Thron was very well known for his work on will take the responsibility of editing OPSF continued fractions and his book Continued Frac- SIAM Activity Group gang Thron made several important contributions On in the convergence theory for continued fractions. Orthogonal Polynomids and Special Functions Approximately one third of his publications have http://math.nist.gov/opsf been devoted to continued fractions. A recent look A on MathSciNet revealed 142 publications by Wolf- Elected Officers gang Thron, and Zentralblatt MATH even gives DANIELW. LOZIER,Chair 153 publications. Thron has at least four publica- WALTERVAN ASSCHE,Vice Cbair tions with more than 50 citations: the paper Ac- FRANCISCOMARCELLAN, Program Director celerating convergence of limit periodic continued PETERCLARKSON , Secretary fractions K(a,/l) (Numer. Math. 34 (1980), 155- Appointed Officers 170) with H. Waadeland, the well written survey Moment theory, orthogonal polynomials, quadra- RENATOALVAREZ-NODARSE, Co-Editor of the Newsletter ture, und continued fractions associated with the RAFAELJ. YANEz, Co-Editor of the Newsletter unit circle (Bull. London Math. Soc. 21 (1989), MARTINE. MULDOON,Editor of tbe OP-SF Net 113-152) with W. B. Jones and 0. Njastad, the BONITASAUNDERS, Webmaster paper A strong Stieltjes moment problem (Trans. Amer. Math. Soc. 261 (1980), 503-528) with W. A B. Jones and H. Waadeland, and the related Or- THEPURPOSE of the Activity Group is thogonal Laurent polynomials und the strong Ham- -to promote basic research in orthogonal polyno- mids and special functions; to further the application burger moment problem (J. Math. Anal. Appl. 98 of this subject 'in other parts of mathematics, and in (1984), 528-554) with W. B. Jones and 0. Njb- science and industry; and to encourage and support tad, clearly have been very influential. Thron also the exchange of information, ideas, and techniques has his own continued fraction: the T-fraction, between workers in this field, and other mathemati- cians and scientists. which is related to two point Pad6 approximation and Laurent orthogonal polynomials. Wolfgang Thron started his long career at the University of Colorado in Boulder in 1954 fill- tions, Analytic Theory und Applications (with W. ing in the vacancy in mathematics when Albert B. Jones), which appeared in 1980, is one of the Edrei moved to Syracuse University. He had 21 most valuable books on the subject. Wolf Thron Ph. D. students and wrote two books: in 1966 a book on Topological Structures, and in 1980 was born on August 17, 1918 in Ribnitz (Ger- the book with Bill Jones on continued fractions, many). In 1936 Thron first was sent to the ETH in which was mentioned earlier. Thron spent a lot Zürich (Switzerland) and then to Princeton Uni- versity, where his aunt and uncle (Herman Weyl) of time at foreign universities: in 1957-58 he was could keep an eye on him and lend him a help- at the University of Miinich, close to Oscar Per- ron, in 1962-63 and in 1974-75 he was at Pun- ing hand if necessary. After his B.A. degree from jab University in Chandigarh, India, in 1966-67 he Princeton in 1939 he held a teaching fellowship at Washington State University in Pullman, and was at Mindanao State University in the Philip- pines, in 1970-71 he was at Erlangen University a year later he accepted a teaching fellowship for in Germany, and in 1978-79, 1982-83, 1987 he graduate study at the mathematics department of worked at the University of Trondheim in Norway. Rice University, where he worked under supervi- sion of Walter Leighton. Thron's thesis was on There he continued a long and productive col- laboration with Lisa Jacobsen (now Lorentzen) parabolic convergence regions for continued frac- , Olav Njastad and Haakon Waadeland. Thron be- tions and his results (published in 1942 and 1943) came Professor Emeritus upon his retirement in significantly improved the original parabola the- In recognition of his outstanding work in orem of W. T. Scott and H. S. Wall, which ap- 1985. peared in 1940. During the next six decades Wolf- continued fractions and related topics, an inter- national conference was held at the University of ing Committee and the Fund for Contributing to the Deuel- Colorado in June, 1988 at the occasion of his 70th opment of Mathematical Science were handed to the writer birthday. The proceedings were published in the M. Soroko (the author of the novel Krawtchouk Kolyma theorem: Kolyma is the river in East Siberia where the Rocky Mountain Journal of Mathematics, volume camp was in which Kravchuk has perished) , V. Groza 21 (1991), and included in these proceedings was a (for research on Krawtchouk q-polynomials and Meixner- description of Thron's life and work written by his Krawtchouk q-functions), V. Savva and V. Zelenkov (for former student and long time collaborator W. B. the study of the Krawtchouk oscillator) and S. Lukashuk Jones (W. J. Thron on his 70th birthday, Rocky (a school teacher, founder of the museum the Kravchuk's Mountain J. Math. 21 (1991), 7-23), which in- native village) . cludes a list of his Ph. D. students and 116 pa- There were four sections at the conference: pers (up to 1990). Most of the information in the present obituary is taken from this source and 1. Differential and Integral Equations, and their Appli- from obituaries that were sent to me by Bill Jones. cations. 2. Algebra, Geometry. Mathematical and Numerical Walter Van Assche Analysis. ([email protected] . ac .be) 3. Probability Theory and Mathematical Statistics. Reports from Meetings and Conferences 4. History and Techniques of Mathematical Tesching. 1. IXth International Scientific Kravchuk Confer- Below we list some talks devoted to orthogonal polynomi- ence. Kyiv (Ukraine), May 16-19, 2002 als and special functions. Kachanovski I.: Mykhailo Krawtchouk and the inven- The conference took place from May 16 to May 19,2002 tion of the electronic computer. at the National Technical University of Ukraine (Kyiv). About 700 scientists of 20 countries were present. Burjakov A. N. et al.: On the solution of thermoelas- ticity problems by using integral transforms, methods Many FSU (Former Soviet Union) countries have been of dual equations, special functions including Struve searching for national self-identification during the past functions. decade. The narne of Mykhailo Kravchuk (Krawt~houk)~ has a particular meaning for independent Ukraine. He was a mathematician with an established scientific reputation Zelenkov V. On one generalization of Krawtchouk who become a victim of Stalin's reprisals, and as the author polynomials. of contemporary Ukrainian mathematical terminology he became a symbolical figure. Kirillova T. V. et al.: About one representation of Krawtchouk polynomials. The opening ceremonies of the Kravchuk conferences al- ways had a very solemn character, but now it had a spe- Fisher B., Jolevsaka-Tuneska B., Kilicman A.: On cial character because 2002 is 110 years &er the birth- defining the incomplete gamma-function. day of the scientist. There were recollections about M. Kravchuk, a performance of musicians and a chorus. The Hriptun M. D.: Group-theoretic interpretation of political scientist I. Kachanovski told about the unique some properties of a generalization of cylindrical func- role that Mykhailo Kravchuk played in the invention of tions. the electronic computer. It was announced that one of streets in Kyiv this year will be called after academician Groza V. A.: q-analog of the Burchnall Chaundy's M. Kravchuk. And finally a new book was presented con- formula. taining selected Papers by M. Kravchuk. For the first time the awards established by the Organiz- The participants are grateful to academician M. Zgurovski, the chairman of the Organizing Com- lI will use the spelling Kravchuk when I mean the surname and Kmwtchouk when referring to Krawtchouk polynomials and func- mittee, and certainly also to Nina Virchenko, the initiator tions. of the Kravchuk conferences, long-term contributor and propagandist of Kravchuk's scientific inheritance and there will be poster sessions, and several software demon- biography professor, for her warm hospitality. The next strations (particularly of computer algebra and numerical conference will take place in 2004.