Richard Askey
Encyclopedia
Richard Allen Askey 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. 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. He was elected a Fellow of the American Academy of Arts and Sciences
in 1993. In 1999 he was elected to the National Academy of Sciences
.
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."
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his expertise in the area of special functions. The Askey–Wilson polynomials
Askey–Wilson polynomials
In mathematics, the Askey–Wilson polynomials are a family of orthogonal polynomials introduced by as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme...
are an important schematic in organising the theory of special polynomials (his work with James A. Wilson). The Askey–Gasper inequality
Askey–Gasper inequality
In mathematics, the Askey–Gasper inequality is an inequality for Jacobi polynomials proved by and used in the proof of the Bieberbach conjecture.-Statement:...
for Jacobi polynomials
Jacobi polynomials
In mathematics, Jacobi polynomials are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight ^\alpha ^\beta on the interval [-1, 1]...
is essential in de Brange's
Louis de Branges de Bourcia
Louis de Branges de Bourcia is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges' theorem...
famous proof of the Bieberbach conjecture.
Askey earned a B.A. at Washington University in 1955, an M.A. at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1956, and a Ph.D. at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1961. After working as an instructor at Washington University (1958–1961) and University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
(1961–1963), he joined the faculty of the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
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. He was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1993. In 1999 he was elected to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
.
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."
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.