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 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 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 کاملComputer algebra and Umbral Calculus
Rota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We review this theory and some of its generalizations in light of our computer implementation (Maple V.3). A Mathematica version of this package is being developed in parallel.
متن کاملRota’s Umbral Calculus and Recursions
Umbral Calculus can provide exact solutions to a wide range of linear recursions. We summarize the relevant theory and give a variety of examples from combinatorics in one, two and three variables.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/367