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# Richard Askey

Richard Allen Askey (born June 4, 1933) is an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials are an important schematic in organising the theory of special polynomials (his work with James A. Wilson). The Askey-Gasper inequality for Jacobi polynomials is essential in de Brange's famous proof of the Bieberbach conjecture.

Askey earned a B.A. at Washington University in 1955, an M.A. at Harvard University in 1956, and a Ph.D. at Princeton University in 1961.[1] After working as an instructor at Washington University (1958–1961) and University of Chicago (1961–1963), he joined the faculty of the University of Wisconsin–Madison in 1963 as an Assistant Professor of Mathematics. He became a full professor at Wisconsin in 1968, and since 2003 has been a professor emeritus. Askey is a Fellow of the American Academy of Arts and Sciences and was a Guggenheim Fellow, 1969–1970. In 1999 he was elected to the National Academy of Sciences.[2]

Askey[3] explained why hypergeometric functions appear so frequently in mathematical applications: "Riemann showed that the requirement that a differential equation have regular singular points at three given points and every other complex point is a regular point is so strong a restriction that the differential equation is the hypergeometric equation with the three singularities moved to the three given points. Differential equations with four or more singular points only infrequently have a solution which can be given explicitly as a series whose coefficients are known, or have an explicit integral representation. This partly explains why the classical hypergeometric function arises in many settings that seem to have nothing to do with each other. The differential equation they satisfy is the most general one of its kind that has solutions with many nice properties."

Works

* Orthogonal polynomials and special functions, Richard Askey, SIAM, 1975.

* Special functions, by George E. Andrews, Richard Askey, and Ranjan Roy, Encyclopedia of Mathematics and Its Applications, The University Press, Cambridge, 1999.[4]

References

1. ^ Richard Askey at the Mathematics Genealogy Project

2. ^ Askey biography

3. ^ Askey, R.; Koornwinder, T.H.; Schmepp. W. (eds.). Special functions: group theoretical aspects and applications. Reidel. ISBN 1-4020-0319-6. http://books.google.com/books?isbn=1402003196.

4. ^ Wimp, J. (2000). "Special functions (review)". Bull. AMS 37: 499-510. http://www.ams.org/journals/bull/2000-37-04/S0273-0979-00-00879-X/home.html.

External links

* Personal web page.

* The Askey-scheme of hypergeometric polynomials and its q-analogue by Koekoek & Swarttouw

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