The umbral calculus
نویسندگان
چکیده
منابع مشابه
Formal Calculus and Umbral Calculus
We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial “associativity” property of an im...
متن کاملAlgebras and the Umbral Calculus ∗
We apply Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of λ-umbral calculi parameterized by λ in the base ring.
متن کاملApplied Umbral Calculus
Common ground to the three concepts are special polynomial sequences, called She er sequences. A polynomial sequence (sm (x))m2N0 is a sequence of polynomials sm (x) 2 K [x] such that deg sm = m, s0 6= 0. It is convenient to de ne sm = 0 for negative m. The coe cient ring K is assumed to be an integral domain. For this introduction to Finite Operator Calculus it su ces to choose K as R [!], the...
متن کاملUniversal Constructions in Umbral Calculus
Modern umbral calculus is steadily approaching maturity, as applications develop in several areas of mathematics. To maximize this utility it is important to work in the most general (as opposed to the most abstract) setting. The origins of the 19th century theory lie in analysis. In a beautiful recent article [13] Rota and Taylor have returned to these roots, and their bibliography details man...
متن کاملApplications of the Classical Umbral Calculus
ai. Blissard’s notation has been known variously as Lucas’s method, the symbolic method (or symbolic notation), and the umbral calculus. We shall use Rota and Taylor’s term “classical umbral calculus” [36] to distinguish it from the more elaborate mathematical edifice that the term “umbral calculus” has come to encompass [31, 32, 34]. The goal of this article is to show, by numerous examples, h...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1978
ISSN: 0001-8708
DOI: 10.1016/0001-8708(78)90087-7