mathematics

Mourad Ismail

Mourad Ismail is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mourad Ismail rather than just read about it. In short: Mourad E. H.

Key takeaways

Mourad Ismail belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mourad Ismail to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mourad Ismail from memory before moving on to harder problems.

Reference excerpt

Mourad E. H. Ismail (Arabic: مُراد اسماعيل; born April 27, 1944, in Cairo, Egypt) is a mathematician working on orthogonal polynomials and special functions. Ismail received his bachelor's degree from Cairo University. He holds Masters and doctorate degrees from the University of Alberta. He worked at and visited several universities. Currently he is a visiting professor at the University of Louisiana. Before he held a research professorship at the University of Central Florida and a Distinguished Scientist Fellowship at King Saud University in Saudi Arabia. Ismail is a fellow of the American Mathematical Society and the Institute of Physics. 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. Mourad Ismail works in the area of special functions, orthogonal polynomials and their applications. His research also touches upon approximation theory and continued fractions. Most of Ismail's work is joint with other mathematicians and physicists and some of his papers are interdisciplinary. He worked on infinite divisibility problems in probability 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 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. Ismail is also interested in the combinatorial theory of orthogonal polynomials and their linearization coefficients.

Publications Ismail, Mourad E. H. (2005), Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, ISBN 978-0-521-78201-2

Illustrations

Worked examples

Example 1 — a first encounter with Mourad Ismail

Start with the simplest possible case. Write down what Mourad Ismail claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mourad Ismail before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mourad Ismail ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mourad Ismail

In research: Mourad Ismail appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mourad Ismail in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mourad Ismail is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century American mathematicians, 20th-century Egyptian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mourad Ismail outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mourad Ismail in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mourad Ismail means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mourad Ismail out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mourad Ismail in simple terms?

Mourad E. H.

Why does Mourad Ismail matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mourad Ismail?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mourad Ismail.