mathematics

Wolfgang Hahn

Wolfgang Hahn 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 Wolfgang Hahn rather than just read about it. In short: Wolfgang Hahn (April 30, 1911 – January 10, 1998) was a German mathematician who worked on special functions, in particular orthogonal polynomials. He introduced Hahn polynomials, Hahn difference, Hahn q-addition (or Jackson-Hahn-Cigler q-addition), and the Hahn–Exton q-Bessel function.

Key takeaways

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

Reference excerpt

Wolfgang Hahn (April 30, 1911 – January 10, 1998) was a German mathematician who worked on special functions, in particular orthogonal polynomials. He introduced Hahn polynomials, Hahn difference, Hahn q-addition (or Jackson-Hahn-Cigler q-addition), and the Hahn–Exton q-Bessel function. He was an honorary member of the Austrian Mathematical Society.

References Kappel, F. (1982), "Wolfgang Hahn---an address in honour of his 70th birthday", in Kappel, F.; Schappacher, W. (eds.), Evolution equations and their applications (Schloss Retzhof, 1981), Res. Notes in Math., vol. 68, New York: Pitman, pp. xi–xvi, ISBN 978-0-273-08567-6, MR 0668374 "Professor Dr. Wolfgang Hahn", Journal of Mathematical and Physical Sciences, 18: Si–Svi, 1983, ISSN 0047-2557, MR 0753936 "Nachruf auf Wolfgang Hahn" (PDF), Internationale Mathematische Nachrichten, 181: 2–12, August 1999

External links Wolfgang Hahn at the Mathematics Genealogy Project Pictures of Wolfgang Hahn from Oberwolfach

Illustrations

Worked examples

Example 1 — a first encounter with Wolfgang Hahn

Start with the simplest possible case. Write down what Wolfgang Hahn 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 Wolfgang Hahn 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 Wolfgang Hahn 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 Wolfgang Hahn

In research: Wolfgang Hahn 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 Wolfgang Hahn 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: Wolfgang Hahn is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1911 births, 1998 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Wolfgang Hahn 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 Wolfgang Hahn in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wolfgang Hahn 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 Wolfgang Hahn out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wolfgang Hahn in simple terms?

Why does Wolfgang Hahn 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 Wolfgang Hahn?

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 Wolfgang Hahn.