mathematics

James Alexander Shohat

James Alexander Shohat 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 James Alexander Shohat rather than just read about it. In short: James Alexander Shohat (a.k.a. Jacques Chokhate (or Chokhatte), 18 November 1886, Brest-Litovsk – 8 October 1944, Philadelphia) was a Russian-American mathematician at the University of Pennsylvania who worked on the moment problem.

Key takeaways

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

Reference excerpt

James Alexander Shohat (a.k.a. Jacques Chokhate (or Chokhatte), 18 November 1886, Brest-Litovsk – 8 October 1944, Philadelphia) was a Russian-American mathematician at the University of Pennsylvania who worked on the moment problem. He studied at the University of Petrograd and married the physicist Nadiascha W. Galli, the couple emigrating from Russia to the United States in 1923. He was an Invited Speaker of the ICM in 1924 at Toronto.

Selected works Shohat, J. (1927). "On a general formula in the theory of Tchebycheff polynomials and its applications". Trans. Amer. Math. Soc. 29 (3): 569–583. doi:10.1090/s0002-9947-1927-1501405-8. MR 1501405. Shohat, J. A. (1927). "A simple method for normalizing Tchebycheff polynomials and evaluating the elements of the allied continued fractions". Bull. Amer. Math. Soc. 33 (4): 427–432. doi:10.1090/s0002-9904-1927-04396-8. MR 1561395. with J. Sherman: Shohat, J.; Sherman, J. (1932). "On the numerators of the continued fraction". Proc Natl Acad Sci U S A. 18 (3): 283–287. doi:10.1073/pnas.18.3.283. PMC 1076208. PMID 16587678. "On the development of functions in a series of polynomials". Bull. Amer. Math. Soc. 41 (2): 49–82. 1935. doi:10.1090/s0002-9904-1935-06007-0. MR 1563024. Shohat, J. (1937). "Mechanical quadratures, in particular, with positive coefficients". Trans. Amer. Math. Soc. 42 (3): 461–496. doi:10.1090/s0002-9947-1937-1501930-6. MR 1501930. Shohat, J. (1939). "A differential equation for orthogonal polynomials". Duke Math. J. 5 (2): 401–417. doi:10.1215/s0012-7094-39-00534-x. MR 1546133. with J. D. Tamarkin: The problem of moments. Mathematical Surveys, vol. 1. New York: AMS. 1943. OCLC 622772715. "On van der Pol's and non-linear differential equations". J. Appl. Phys. 15 (7): 568–574. 1944. doi:10.1063/1.1707470.

See also Shohat expansion Shohat–Favard theorem

References

External links James Alexander Shohat at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with James Alexander Shohat

Start with the simplest possible case. Write down what James Alexander Shohat 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 James Alexander Shohat 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 James Alexander Shohat 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 James Alexander Shohat

In research: James Alexander Shohat 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 James Alexander Shohat 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: James Alexander Shohat is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1886 births, 1944 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James Alexander Shohat 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 James Alexander Shohat in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what James Alexander Shohat 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.
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Frequently asked questions

What is James Alexander Shohat in simple terms?

Why does James Alexander Shohat 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 James Alexander Shohat?

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 James Alexander Shohat.