An expert in special functions, Prof Richard Askey from Wisconsin-Madison elaborates some useful extensions of the binomial theorem, one of the results being the Rogers-Ramanujan identities which become essential to some works in physics.
The binomial theorem is ancient, but some useful extensions of it have been found in the last two hundred years. Two of these will be described and some of the results one can obtain from them will be outlined. Two results are identities known as the Rogers-Ramanujan identities. These were discovered by L. J. Rogers, but ignored until Srinivasa Ramanujan found but could not prove them. The surprising story of how these arose in the 1890s and then turned out to be essential in some work in physics in the 1980s will be described.
About the speaker
Professor Richard Askey obtained his PhD from Princeton University in 1961 and was the John Bascom Professor of Mathematics in University of Wisconsin, Madison before he retired and became Professor Emeritus in 2003. Amongst the many honours that Professor Askey received, he was a Guggenheim Fellow (1969-1970), honorary Fellow of Indian Academy of Sciences, a Fellow of American Academy of Arts and Sciences and National Academy of Sciences.
Professor Askey played a leading role in rejuvenating the widely applied, but mathematically ailing subjects of special functions and orthogonal polynomials in 1970s. Special functions were known and studied by Bernoulli, Euler and Gauss, and are known to have numerous applications in mathematics in particular, and in science in general.Askey's worked gave a new imputes to the subject during the 1970s and 1980s by introducing new ideas that include the well-known Askey-scheme, which is a schematic diagram of classical and orthogonal polynomials, positivity sums and integrals, evaluating certain beta integrals, Askey-Wilson polynomials, etc. A positivity sum result about Jacobi polynomials obtained by Askey and Gasper in 1976 was instrumental in de Branges' celebrated proof of the long standing Bieberbach conjecture in 1984.
Professor Askey was an International Congress of Mathematicians speaker in 1983 and he also served in the editorial board of SIAM Journal of Mathematical Analysis for over twenty years. Besides mathematical research, Professor Askey has great interest in history of mathematics and served on the Committee on Mathematics History of American Mathematical Society from 1987 to 1991, and has been active in school mathematics education in US.
