An algebraic approach to Sheffer polynomial sequences

被引：32

作者：

Costabile, Francesco Aldo ^{[1
]}

Longo, Elisabetta ^{[1
]}

机构：

[1] Univ Calabria, Dept Math, I-87036 Arcavacata Di Rende, Italy

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2014年 / 25卷 / 04期

关键词：

Sheffer; polynomials; determinant; INTERPOLATORY PROBLEMS; RIORDAN GROUP;

D O I：

10.1080/10652469.2013.842234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A matrix approach to Sheffer polynomial sequences is proposed; in particular, two different determinantal forms of Sheffer sequences are given, the one as the function of a polynomial sequence of binomial type and the other as the function of the canonical base x(i). The equivalence with the classical definitions of Sheffer and Roman and Rota is proven. Then, elementary matrix algebra tools are employed to reveal the known and unknown properties of Sheffer polynomials. Finally, classical and non-classical examples are also considered.

引用

页码：295 / 311

页数：17

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