Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers

被引：4

作者：

Dagli, Muhammet Cihat ^{[1
]}

机构：

[1] Akdeniz Univ, Fac Sci, Dept Math, TR-07058 Antalya, Turkey

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 05期

关键词：

Bell polynomial of the second kind; Boole number; Boole polynomial; determinantal expression; explicit formula; generating function; Hessenberg determinant; Peters number; Peters polynomial; recursive relation; BELL POLYNOMIALS; COMBINATORIAL NUMBERS; CLOSED FORMULAS; BOOLE NUMBERS; EXPRESSIONS; BERNOULLI; FAMILY; TERMS; FORMS;

D O I：

10.1002/mma.7941

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, with the help of the Faa di Bruno formula and an identity for the Bell polynomials of the second kind, we find several explicit formulas for the Peters polynomials and numbers. Also, we present determinantal representations for the Peters polynomials and numbers by virtue of a general derivative formula for the ratio of two differentiable functions. Moreover, we give several recursive relations for the Peters polynomials and numbers. As an application, we establish alternative recursive relations for them with the aid of a recursive relation for the Hessenberg determinants. These results cover counterparts for the Boole polynomials and numbers.

引用

页码：2582 / 2591

页数：10

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