Mourad E. H. Ismail (born April 27, 1944, in

Cairo Cairo ( ; , ) is the Capital city, capital and largest city of Egypt and the Cairo Governorate, being home to more than 10 million people. It is also part of the List of urban agglomerations in Africa, largest urban agglomeration in Africa, L ...

Egypt Egypt ( , ), officially the Arab Republic of Egypt, is a country spanning the Northeast Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via the Sinai Peninsula. It is bordered by the Mediterranean Sea to northe ...

) is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

working on

orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...

and

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

. Ismail received his bachelor's degree from

Cairo University Cairo University () is Egypt's premier public university. Its main campus is in Giza, immediately across the Nile from Cairo. It was founded on 21 December 1908;"Brief history and development of Cairo University." Cairo University Faculty of En ...

. He holds Masters and doctorate degrees from the

University of Alberta The University of Alberta (also known as U of A or UAlberta, ) is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford, the first premier of Alberta, and Henry Marshall Tory, t ...

. He worked at and visited several universities. Currently he holds a research professorship at the

University of Central Florida The University of Central Florida (UCF) is a public university, public research university with its main campus in unincorporated area, unincorporated Orange County, Florida, United States. It is part of the State University System of Florida. ...

and a Distinguished Scientist Fellowship at

King Saud University King Saud University (KSU, ) is a public university in Riyadh, Saudi Arabia. Established in 1957 by King Saud bin Abdulalziz to address the country's skilled worker shortage, it is the first university in Saudi Arabia. It was known as Riyadh U ...

Saudi Arabia Saudi Arabia, officially the Kingdom of Saudi Arabia (KSA), is a country in West Asia. Located in the centre of the Middle East, it covers the bulk of the Arabian Peninsula and has a land area of about , making it the List of Asian countries ...

. Ismail is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

List of Fellows of the American Mathematical Society
retrieved 2014-12-17 and the

Institute of Physics The Institute of Physics (IOP) is a UK-based not-for-profit learned society and professional body that works to advance physics education, physics research, research and applied physics, application. It was founded in 1874 and has a worldwide ...

. He is among the ISI highly cited scientists. He served on the editorial boards of several journals including ''Constructive Approximation'', ''Journal of Approximation Theory'', ''Journal of Physics A'', and ''The Ramanujan Journal''. He published over 290 research articles, one book and edited several books. Most of Ismail's work is joint with other mathematicians and physicists and some of his papers are interdisciplinary. Mourad Ismail works in the area of

special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

and their applications. His research also touches upon

approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

and

continued fraction A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, ...

s. He worked on

infinite divisibility Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). One may speak of infinite divisibility, or the lack thereof, of matter ...

problems in

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

that led to questions about monotonicity properties of special functions. He also worked on monotonicity and inequalities for zeros of orthogonal polynomials. He made several contributions to the

asymptotic theory In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as bec ...

of orthogonal polynomials. He also studied moment problems and found the orthogonality measure for several orthogonal polynomials. This includes the ''q''-ultraspherical polynomials (also known as the Askey–Ismail or Rogers–Askey–Ismail polynomials), the random walk polynomials (also known as the Askey–Ismail polynomials), the Al-Salam–Ismail polynomials, and the Chihara–Ismail polynomials. Ismail also worked on ''q''-series and

Rogers–Ramanujan identities In mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered and proved by , and were subsequently rediscovered (without a proof) by Srin ...

. Ismail is also interested in the combinatorial theory of orthogonal polynomials and their linearization coefficients.

Publications

References

Mourad E.H. Ismail home page

De Gruyter Open

Microsoft Academic Research

Distinguished Scientist Fellowship Program

External links

* * * {{DEFAULTSORT:Ismail, Mourad E. H. Living people 20th-century Egyptian mathematicians 20th-century American mathematicians 21st-century American mathematicians 1944 births Fellows of the American Mathematical Society University of Alberta alumni

Publications

See also

References

External links