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위키데이터

• ID : Q1055314

말뭉치

1. In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them.
2. In the 1970s, Steven Roman, Gian-Carlo Rota, and others developed the umbral calculus by means of linear functionals on spaces of polynomials.
3. {\displaystyle L((z+x)^{n})} , that is, move the n from a subscript to a superscript (the key operation of umbral calculus).
4. Then we define sequences analogous to Boas-Buck polynomial sequences and extend the main results of the nonclassical umbral calculus on such sequences.
5. Classical umbral calculus was introduced by Blissard in the 1860’s and later studied by E. T. Bell and Rota.
6. In her PhD thesis, M. Héraoua has given an umbral calculus on the so called ring of formal differential operators which has a coalgebra structure.
7. Have you come across the umbral calculus?
8. They have been studied by various means like combinatorial methods, generating functions, differential equations, umbral calculus techniques, p-adic analysis, and probability theory.
9. The purpose of the present paper is to study the degenerate Bell polynomials and numbers by means of umbral calculus and generating functions.
10. The novelty of this paper is that they are further explored by employing a different method, namely umbral calculus.
11. In addition, we briefly state some basic facts about umbral calculus.
12. A set-theoretic interpretation of the umbral calculus.
13. Recently, the umbral calculus has been extended in several directions.
14. The purpose of this paper is to study degenerate Bell polynomials by using umbral calculus and generating functions.
15. Umbral calculus originated as a method for discovering and proving combinatorial identities, but is developed in a more general form in this book.
16. Umbral calculus was developed in the 1800s and is attributed to various combinations of John Blissard, Édouard Lucas, and James Joseph Sylvester.
17. The early days of umbral calculus were like the early days of the infinitesimal calculus: in the hands of skilled practitioners it produced correct results, but no one was sure why it worked.
18. E. T. Bell was fascinated by the umbral calculus and attempted a revival of it in the 1930s and 1940s, but still no one understood it well.
19. This research was carried out in part at the Conference on Umbral Calculus and Hopf Algebras held in Norman, May 15–20, 1978.
20. The aim of these lectures is to give an introduction to combinatorial aspects of Umbral Calculus.
21. Seen in this light, Umbral Calculus is a theory of polynomials that count combinatorial objects.
22. In the rst two lectures we present the basics of Umbral Calculus as presented in the seminal papers Mullin and Rota (1970) and Rota, Kahaner, and Odlyzko (1973).
23. In the third lecture we present an extension of the Umbral Calculus due to Niederhausen for solving recurrences and counting lattice paths.
24. In the important Section 4.1, which contains the algebraic rules for the two q-additions and the infinite alphabet, we introduce the q-umbral calculus in the spirit of Rota.
25. One should keep in mind that each plays three roles in the umbral calculus: a formal power series, a linear functional, and a linear operator.
26. In this paper, we study some properties of umbral calculus related to the Appell sequence.
27. Hence Umbral Calculus was freed of its magical aura and put on a solid basis.
28. Further details on how to apply Umbral Calculus are necessarily more technical in nature.
29. Umbral Calculus can be used as a tool for solving recursions, if the exact solutions to such recursions are Sheffer sequences.
30. We will show that in many applications Umbral Calculus provides the generating function too; the more interesting problems may be those where that is not the case.
31. The Umbral Calculus is built on shift-in v arian t op erators.