2 4 A ug 1 99 9 Umbral presentations for polynomial sequences
نویسنده
چکیده
Using random variables as motivation, this paper presents an exposition of formalisms developed in [RT1, RT2] for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials.
منابع مشابه
9 F eb 1 99 5 Maple Umbral Calculus Package
Rota’s Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We have developed a Maple package that implements Rota’s Umbral Calculus and some of its generalizations. A Mathematica version of this package is being developed in parallel.
متن کاملUmbral presentations for polynomial sequences
Using random variables as motivation, this paper presents an exposition of formalisms developed in [RT1, RT2] for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials.
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متن کاملAn Algebraic Exposition of Umbral Calculus with Application to General Linear Interpolation Problem – a Survey
A systematic exposition of Sheffer polynomial sequences via determinantal form is given. A general linear interpolation problem related to Sheffer sequences is considered. It generalizes many known cases of linear interpolation. Numerical examples and conclusions close the paper. 1. The modern umbral calculus In the 1970s Rota and his collaborators [17,19,20] began to construct a completely rig...
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Sequences of polynomials, verifying the (▭), nowadays called Appell polynomials, have been well studied because of their remarkable applications not only in different branches of mathematics ([2], [3]) but also in theoretical physics and chemistry ([4], [5]). In 1936 an initial bibliography was provided by Davis (p. 25[6]). In 1939 Sheffer ([7]) introduced a new class of polynomials which exten...
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