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6-3.Pdf, 298 Kb Orthogonal Polynomials and Special Functions SIAM Activity Group on Orthogonal Polynomials and Special Functions ???? Newsletter ???? Published Three Times a Year June 1996 Volume 6, Number 3 Contents of members of our Activity Group. In particu- lar, both the Chair, Charles Dunkl, and the Vice From the Editor . 1 Chair, Tom H. Koornwinder, now have their own Memorial Note about Waleed Al-Salam . 2 WWW home pages whose addresses are listed on Memorial Note about Lawrence C. Biedenharn . 3 page 19. Reports from Meetings and Conferences . 4 Forthcoming Meetings and Conferences . 6 I invite everybody to consult some of the Books and Journals . 12 WWW pages which can give interesting infor- Software Announcements . 15 Problems and Solutions . 15 mation about orthogonal polynomials and special Miscellaneous . 18 functions. Rather than looking a formula up in a How to Contribute to the Newsletter . 18 mathematical dictionary, the desired information Activity Group: Addresses . 19 could be online available to you! Steven Finch is developing a WWW page on L P O N A L Y Favorite Mathematical Constants and their inter- O N G O O M relations which was announced in the last issue H I A T of the Newsletter. His site includes a wealth of L R SIAM S O mathematical knowledge and can be visited at Activity Group http://www.mathsoft.com/cgi-shl/constant.bat. S S P E Est. 1990 N C O At http://www.cecm.sfu.ca/projects/ISC/ you I I A C T L F U N have access to the Inverse Symbolic Calculator that looks up in a huge database to identify deci- mal numbers and uses modern algorithmic meth- ods to generate algebraic identities between sev- From the Editor eral of them. Using these methods, the formula µ ¶ µ ¶ The electronic media, and, in particular, the X1 4 2 1 1 1 k ¼ = ¡ ¡ ¡ World Wide Web, influence the daily work of re- 8k + 1 8k + 4 8k + 5 8k + 6 16 searchers all over the world more and more. This k=0 is reflected, for example, in the continually in- was discovered recently; it gives the opportunity creasing number of personal WWW home pages to calculate far out coe±cients of ¼'s hexadecimal June 1996 Orthogonal Polynomials and Special Functions Newsletter 2 SIAM Activity Group Wilson scheme, equipped with any standardiza- on tion you may wish to use; see also p. 15. Im- Orthogonal Polynomials and Special Functions plementations of the editor are used for this 3 purpose. This interface can be visited at Elected O±cers http://www.can.nl/~renes/CAOP.html. Charles Dunkl, Chair You see there is a lot to discover! Strolling Tom H. Koornwinder, Vice Chair through these pages will furthermore link you to Willard Miller, Program Director many other interesting sites. I hope you all can Nico M. Temme, Secretary take advantage of the possibilities which these new Appointed O±cers media o®er! Wolfram Koepf, Editor of the Newsletter If you know about interesting WWW pages con- Martin E. Muldoon, Webmaster cerning orthogonal polynomials and special func- 3 tions that I did not mention, please submit the The purpose of the Activity Group is corresponding addresses to the Editor. Our mem- |to promote basic research in orthogonal polyno- bers should receive such information. mials and special functions; to further the application of this subject in other parts of mathematics, and in May 31, 1996 Wolfram Koepf science and industry; and to encourage and support the exchange of information, ideas, and techniques between workers in this ¯eld, and other mathemati- cians and scientists. Memorial Note about Waleed Al-Salam 1926-1996 Friends and colleagues are saddened by news of expansion without the computation of early ones, the passing, a few months short of his 70th birth- using single precision arithmetic! day, of Waleed Al-Salam, Professor Emeritus of Mathematics at the University of Alberta. Born Victor Adamchik and Stan Wagon present a on July 15, 1926 in Baghdad, Iraq, he died on deduction of a generalization of the above formula April 14, 1996 in Edmonton, Alberta, Canada. using symbolic computation on their WWW page http://www.wri.com/~victor/articles/pi/pi.html. Waleed studied at the University of California, Berkeley, earning a Bachelor's degree in Engineer- David H. Bailey and Simon Plou®e who ing Physics in 1950 and a M.A. in Mathematics have discovered the above representation to- in 1951. He returned to Baghdad as an Instructor gether with Peter Borwein have their own at the College of Science for a few years, before WWW page on Recognizing Real Numbers at enrolling for the Ph.D. at Duke University. He http://www.cecm.sfu.ca/organics/papers/bailey/. completed the degree in 1958 with a thesis On the An archive on Numbers with details about Bessel Polynomials written under the supervision history, theory, applications, as well as printed of Leonard Carlitz. By this time he was already and electronic references can be found at a regular contributor to the periodical literature http://archives.math.utk.edu/subjects/numbers.html with some 20 published articles on a variety of containing e.g., a link to continued fractions. topics in orthogonal polynomials and special func- Concerning families of orthogonal polynomi- tions. als, Ren¶e Swarttouw designed an interface to After completing his Ph.D., Waleed returned Maple which currently enables the generation to the College of Science in Baghdad as Asso- of plots as well as an online computation ciate Professor. Coming back to North America of recurrence, di®erential and di®erence equa- in 1962, he eventually (1966) took a position at tions for orthogonal polynomials of the Askey- the University of Alberta, where he was Professor June 1996 Orthogonal Polynomials and Special Functions Newsletter 3 of Mathematics from 1967 until his retirement in Memorial Note about 1992. Waleed continued to contribute to several Lawrence C. Biedenharn areas related to orthogonal polynomials; his CV lists over 80 articles. Areas covered by his work in- Lawrence C. Biedenharn Jr., 73, a longtime clude characterization theorems (see his survey ar- member of Duke University's physics faculty and ticle in pp. 1{24 of P. Nevai, ed., Orthogonal Poly- an internationally known researcher in theoretical nomials: Theory and Practice, Kluwer, 1990), physics, died Monday, Feb. 12, in Austin, Texas, Turan expressions, generating functions, summa- after a lengthy battle with cancer. He had made tion formulas, q-analogs, and fractional operators. his home in Texas in recent years. He and his collaborators did much work on vari- ous special and generalized systems of orthogonal Biedenharn became the youngest full professor polynomials. The Al-Salam-Carlitz polynomials on the Duke faculty|at age 38|when he was ap- (1965) are still frequently cited; see, e.g., the pa- pointed in 1961. He remained at Duke until 1993, pers of R. Askey and S.K. Suslov in Lett. Math. when he retired as James B. Duke professor of Phys. 29 (1993), 123-132 and J. Phys. A 20 (1993), physics and subsequently moved to the University L693-L698. The Al-Salam-Chihara polynomials of Texas at Austin as adjunct professor. (1976) play an important role in the Askey-Wilson A native of Vicksburg, Miss., he received both scheme of basic hypergeometric orthogonal poly- his bachelor's degree and his Ph.D. from the Mas- nomials. sachusetts Institute of Technology and served in Waleed supervised the Ph.D. work of Bill All- World War II as a Signal Corps o±cer and later away (1972) and Mourad Ismail (1974), and con- on the sta® of Gen. Douglas MacArthur in Japan. ducted joint work with a variety of people at Al- Serving on the faculties of Yale University and berta and elsewhere. In later years, these in- Rice University before coming to Duke, he pub- cluded Ted Chihara, A. Verma, Mourad Ismail lished six books and hundreds of research articles and Waleed's wife, Nadhla Al-Salam, also on the in the ¯elds of nuclear physics and later math- faculty at Alberta, and a member of this Activity ematical physics. He also edited the Journal of Group. Mathematical Physics for many years. On his retirement in 1992, Waleed decided to Biedenharn, Holman, and Louck showed how put his expertise and energy at the disposal of the the classical work on ordinary hypergeometric se- orthogonal polynomials community by starting ries is intimately related to the irreducible rep- and maintaining an ftp site for papers in the area. resentations of the compact group SU(2). Simi- This e®ort prospered and he continued to oversee larly, they found U(n) multiple series generaliza- it until last year when his failing health made it tions of one-variable hypergeometric summation necessary to pass the task to Hans Haubold at the and transformation theorems by comparing two UN O±ce in Vienna. Waleed had been diagnosed ways of computing the matrix elements of multi- with leukemia in 1993 and this was to reduce his plicity free Wigner and Racah coe±cients in U(n). active participation in conferences in subsequent This work was done in the context of the quan- years. Nevertheless, with Nadhla's constant sup- tum theory of angular momentum and the spe- port, he still managed to travel and old and new cial unitary groups SU(n). This work motivated friends were able to bene¯t from his knowledge the far-reaching q-analogs that Milne, Gustafson, and enjoy his optimistic and humorous personal- and their co-workers subsequently found. Appli- ity. cations of this later work include uni¯ed proofs Martin Muldoon of the Macdonald identities, constant term iden- (muldoon@mathstat.yorku.ca) tities, multiple q-beta integrals, U(n + 1) and symplectic generalizations of the Bailey Trans- form and Bailey Lemma, classical matrix inver- sion results, numerous classical summation and June 1996 Orthogonal Polynomials and Special Functions Newsletter 4 transformation theorems for one-variable q-series, high computational power of this approach by giving Rogers-Ramanujan identities, and, ¯nally, new in- one-line proofs of properties of the Bernoulli polyno- ¯nite families of identities for sums of squares in mials.
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  • Curriculum Vita
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