After graduating from Harvard, Askey moved to Princeton University to study for his doctorate. In 1958 he accepted a post of Instructor back at Washington University and he held this position until 1961, the year in which he graduated with his Ph.D. from Princeton University. His next move was to the University of Chicago where he was an Instructor for two years before accepting the post of Assistant Professor of Mathematics at the University of Wisconsin-Madison in 1963. Two years later he was promoted to Associate Professor of Mathematics then, in 1968, he became a full Professor.
It is impossible in an article like this to give much in the way of details of the impressive publications by Askey on the harmonic analysis of special functions, orthogonal polynomials and special functions, and special functions related to group theory. To date over 180 publications are listed under his name. The first of these publications was Weighted quadratic norms and ultraspherical polynomials in 1959 which he wrote jointly with Isidore Hirschman Jr. It appeared in the Transactions of the American Mathematical Society. This was the first of two papers by Askey and Hirschman which completed a programme of research initiated by Hirschman in 1955. In 1965 Askey published On some problems posed by Karlin and Szegő concerning orthogonal polynomials and by this time his major contributions to special functions and orthogonal polynomials was well under way.
Askey published an important book Orthogonal polynomials and special functions in 1975. This work was based on ten lectures that he gave to the National Science Foundation Regional Conference at Virginia Polytechnic Institute and State University in June of 1974. In the book hypergeometric functions, Bessel functions, the Jacobi orthogonal polynomials, the Hahn orthogonal polynomials, Laguerre polynomials, Hermite polynomials, Meixner polynomials, Krawtchouk polynomials and Charlier polynomials all play their part in addition to other orthogonal polynomials and special functions. Askey states clearly in this text why he is interested in special functions:
One studies special functions not for their own sake, but to be able to use them to solve problems.G Gasper, in reviewing Askey's book, states:-
This is one of the best introductions to special functions for mathematicians, scientists, and engineers that I know of.Twenty five years after he gave his series of ten lectures to the National Science Foundation Regional Conference, Askey published another major work on special functions. This 1999 book is co-authored by George E Andrews and Ranjan Roy, and is called simply Special Functions. Published by Cambridge University Press, this new work is six times the length of the earlier one. Bruce C Berndt, reviewing this important book, puts it in context:-
Special functions, which include the trigonometric functions, might be called "useful" functions. For some years, the field was somewhat dormant, but in the past three decades, special functions have returned to the forefront of mathematical research. ... fresh new ideas, in large part due to the authors; the many new uses of special functions; and their connections with other branches of mathematics, physics, and other sciences have played leading roles in this revival. ...If one were to single out one paper by Askey of being of particular importance, it must be the one which contained a result which was used by Louis de Branges in giving his complete proof of the Bieberbach Conjecture in 1984.
The book genuinely reflects the authors' vast accumulated insights. Most notably, the authors demonstrate a superb familiarity with the historical roots of their subject. Many of their historical insights and references could have been provided only by them.
Askey is not only known for his mathematical research, however, for he is also a highly respected writer on mathematical education. Perhaps his most famous article on this topic is Good Intentions are not Enough. He has also served the American Mathematical Society in many ways since he first became a member in 1966, sitting on numerous committees and being Vice President of the Society in 1986-87. In particular, his great interest in the history of mathematics is reflected but the fact that he served on the Committee on Mathematical History from 1987 to 1991.
We have already referred above to his lectures to the National Science Foundation Regional Conference in 1974. He also gave two series of lectures in 1984, namely the University of Illinois Trjitzinsky Lectures and the Pennsylvania State University College of Science Lectures. In 1992 he gave the Turán Memorial Lectures in Budapest.
Among the many honours which have been given to Askey we can mention only a few. He is an Honorary Fellow of Indian Academy of Sciences and a Fellow of American Academy of Arts and Science. He received what might be considered his greatest honour in 1999 when he was elected to the National Academy of Sciences.
Askey has remained at the University of Wisconsin-Madison since his first appointment in 1963, becoming Gabor Szegő Professor of Mathematics in 1986 and John Bascom Professor of Mathematics in 1995.
Article by: J J O'Connor and E F Robertson
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