Richard Askey

Richard "Dick" Askey
Richard Askey in 1977
Born	(1933-06-04) June 4, 1933 St. Louis, Missouri
Nationality	American
Fields	mathematics
Institutions	University of Chicago University of Wisconsin–Madison
Alma mater	Washington University in St. Louis Harvard University Princeton University
Doctoral advisor	Salomon Bochner
Doctoral students	James A. Wilson
Known for	Askey–Wilson polynomials Askey–Gasper inequality

Richard "Dick" Allen Askey (born June 4, 1933) is an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials (introduced by him in 1984 together with James A. Wilson) are on the top level of the (q)-Askey scheme, which organizes orthogonal polynomials of (q-)hypergeometric type into a hierarchy. 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 was a Guggenheim Fellow, 1969–1970, which academic year he spent at the Mathematisch Centrum in Amsterdam. In 1983 he gave an invited lecture at the International Congress of Mathematicians (ICM)^[2] in Warszawa. He was elected a Fellow of the American Academy of Arts and Sciences in 1993.^[3] In 1999 he was elected to the National Academy of Sciences.^[4] In 2009 he became a fellow of the Society for Industrial and Applied Mathematics (SIAM).^[5] In 2012 he became a fellow of the American Mathematical Society.^[6] In December 2012 he received an honorary doctorate^[7] from SASTRA University in Kumbakonam, India.

Askey 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".^[8]

Askey is also very much involved with commenting and writing on mathematical education at American schools. A well-known article by him on this topic is Good Intentions are not Enough.^[9]

Works

• Richard Askey, Orthogonal polynomials and special functions, SIAM, 1975.
• Richard Askey and James Wilson, "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials", Memoirs of the American Mathematical Society 54 (319), 1985: iv+55, doi:10.1090/memo/0319, ISBN 978-0-8218-2321-7, MR 783216 
• George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and Its Applications, The University Press, Cambridge, 1999.^[10]

References

External links

• Personal web page.
• The Askey-scheme of hypergeometric polynomials and its q-analogue by Koekoek & Swarttouw
• Photo gallery on the occasion of Dick Askey's 80th.
• search on author Richard Askey from Google Scholar