Closed form expressions for Appell polynomials

被引:5
|
作者
Adell, Jose A. [1 ]
Lekuona, Alberto [1 ]
机构
[1] Univ Zaragoza, Fac Ciencias, Dept Metodos Estadist, Zaragoza 50009, Spain
来源
RAMANUJAN JOURNAL | 2019年 / 49卷 / 03期
关键词
Appell polynomials; Binomial convolution; Forward difference transformation; Higher order convolution identities; Generalized Bernoulli polynomials; Generalized Apostol-Euler polynomials; APOSTOL-BERNOULLI; EXPLICIT FORMULA; HIGHER-ORDER; EULER; PRODUCTS; IDENTITIES; SUMS; CONVOLUTION;
D O I
10.1007/s11139-018-0026-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation of binomial convolution. As a consequence, we obtain explicit expressions for higher order convolution identities referring to various kinds of Appell polynomials in terms of the Stirling numbers. Applications of the preceding results to generalized Bernoulli and Apostol-Euler polynomials of real order are discussed in detail.
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页码:567 / 583
页数:17
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