H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 58 Citations 11,508 297 World Ranking 301 National Ranking 162

Research.com Recognitions

Awards & Achievements

2015 - Fellow of the American Mathematical Society For contributions to classical analysis and special function theory, as well as for service to the community.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Algebra
  • Quantum mechanics

His main research concerns Orthogonal polynomials, Pure mathematics, Discrete orthogonal polynomials, Hahn polynomials and Wilson polynomials. Mourad E. H. Ismail does research in Orthogonal polynomials, focusing on Jacobi polynomials specifically. The concepts of his Pure mathematics study are interwoven with issues in Discrete mathematics, Recurrence relation and Bessel function.

His work on Discrete orthogonal polynomials is being expanded to include thematically relevant topics such as Classical orthogonal polynomials. His Hahn polynomials research is multidisciplinary, incorporating perspectives in Laguerre polynomials and Rogers polynomials. As a part of the same scientific family, he mostly works in the field of Wilson polynomials, focusing on Gegenbauer polynomials and, on occasion, Algebra, Q analogues and Macdonald polynomials.

His most cited work include:

  • Classical and quantum orthogonal polynomials in one variable (1108 citations)
  • Recurrence Relations, Continued Fractions, and Orthogonal Polynomials (226 citations)
  • A generalization of ultraspherical polynomials (198 citations)

What are the main themes of his work throughout his whole career to date?

Mourad E. H. Ismail mostly deals with Orthogonal polynomials, Pure mathematics, Classical orthogonal polynomials, Discrete orthogonal polynomials and Wilson polynomials. Orthogonal polynomials is a subfield of Combinatorics that Mourad E. H. Ismail tackles. His study looks at the relationship between Pure mathematics and fields such as Monotonic function, as well as how they intersect with chemical problems.

Mourad E. H. Ismail interconnects Discrete mathematics and Laguerre polynomials in the investigation of issues within Classical orthogonal polynomials. His Wilson polynomials research is multidisciplinary, incorporating elements of Macdonald polynomials and Algebra. His Jacobi polynomials study results in a more complete grasp of Mathematical analysis.

He most often published in these fields:

  • Orthogonal polynomials (54.96%)
  • Pure mathematics (41.16%)
  • Classical orthogonal polynomials (37.53%)

What were the highlights of his more recent work (between 2011-2021)?

  • Orthogonal polynomials (54.96%)
  • Classical orthogonal polynomials (37.53%)
  • Pure mathematics (41.16%)

In recent papers he was focusing on the following fields of study:

Orthogonal polynomials, Classical orthogonal polynomials, Pure mathematics, Wilson polynomials and Discrete orthogonal polynomials are his primary areas of study. Mourad E. H. Ismail works in the field of Orthogonal polynomials, focusing on Jacobi polynomials in particular. Within one scientific family, Mourad E. H. Ismail focuses on topics pertaining to Difference polynomials under Classical orthogonal polynomials, and may sometimes address concerns connected to Discrete mathematics.

As a member of one scientific family, Mourad E. H. Ismail mostly works in the field of Pure mathematics, focusing on Function and, on occasion, Entire function and Monotonic function. His research on Wilson polynomials focuses in particular on Askey–Wilson polynomials. His study ties his expertise on Gegenbauer polynomials together with the subject of Discrete orthogonal polynomials.

Between 2011 and 2021, his most popular works were:

  • Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (61 citations)
  • Analytic properties of complex Hermite polynomials (60 citations)
  • The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients (54 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Algebra
  • Quantum mechanics

Mourad E. H. Ismail mainly investigates Orthogonal polynomials, Wilson polynomials, Classical orthogonal polynomials, Discrete orthogonal polynomials and Jacobi polynomials. His Orthogonal polynomials research is multidisciplinary, relying on both Laguerre polynomials, Quantum optics and Algebra. His Wilson polynomials research integrates issues from Quadratic equation, Algebra over a field, Hypergeometric distribution and Algebraic number.

His Classical orthogonal polynomials study introduces a deeper knowledge of Combinatorics. His studies in Discrete orthogonal polynomials integrate themes in fields like Gegenbauer polynomials and Difference polynomials. His Hahn polynomials study deals with Koornwinder polynomials intersecting with Al-Salam–Chihara polynomials.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Top Publications

Classical and quantum orthogonal polynomials in one variable

Mourad E. H. Ismail.
Published in <b>2005</b> in Cambridge New York by Cambridge University Press (2005)

1413 Citations

Recurrence Relations, Continued Fractions, and Orthogonal Polynomials

Richard Askey;Mourad Ismail.
(1984)

328 Citations

A generalization of ultraspherical polynomials

Richard Askey;Richard Askey;Mourad E.-H. Ismail;Mourad E.-H. Ismail.
(1983)

271 Citations

$q$-Hermite polynomials, biorthogonal rational functions, and $q$-beta integrals

M. E. H. Ismail;D. R. Masson.
Transactions of the American Mathematical Society (1994)

196 Citations

The zeros of basic Bessel functions, the functions Jv + ax(x), and associated orthogonal polynomials☆

Mourad E.H Ismail.
Journal of Mathematical Analysis and Applications (1982)

194 Citations

Orthogonal polynomials : theory and practice

Paul G. Nevai;Mourad Ismail.
(1990)

183 Citations

The combinatorics of q -Hermite polynomials and the Askey-Wilson integral

Mourad Ismail;Dennis Stanton;Gerard Viennot.
The Journal of Combinatorics (1987)

178 Citations

Ladder operators and differential equations for orthogonal polynomials

Yang Chen;Mourad E H Ismail.
Journal of Physics A (1997)

157 Citations

A generalization of starlike functions

Mourad E. H Ismail;Edward Merkes;David Styer.
Complex Variables, Theory and Application: An International Journal (1990)

151 Citations

Completely monotonic functions involving the gamma and q-gamma functions

Arcadii Z. Grinshpan;Mourad E. H. Ismail.
Proceedings of the American Mathematical Society (2005)

151 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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