Generating Functions for Special Polynomials and Numbers Including Apostol-Type and Humbert-Type Polynomials

被引：32

作者：

Ozdemir, Gulsah ^{[1
]}

Simsek, Yilmaz ^{[1
]}

Milovanovic, Gradimir V. ^{[2
,3
]}

机构：

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

[2] Serbian Acad Arts & Sci, Beograd, Serbia

[3] Univ Nis, Fac Sci & Math, Nish, Serbia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 03期

关键词：

Generating function; Fibonacci polynomials; Humbert polynomials; Bernoulli polynomials and numbers; Euler polynomials and numbers; Apostol-Bernoulli polynomials and numbers; Apostol-Euler polynomials and numbers; Genocchi polynomials; Stirling numbers; UNIFIED PRESENTATION; BERNOULLI; EULER; FAMILIES;

D O I：

10.1007/s00009-017-0918-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to give generating functions and to prove various properties for some new families of special polynomials and numbers. Several interesting properties of such families and their connections with other polynomials and numbers of the Bernoulli, Euler, Apostol-Bernoulli, Apostol-Euler, Genocchi and Fibonacci type are presented. Furthermore, the Fibonacci-type polynomials of higher order in two variables and a new family of special polynomials (x, y) bar right arrow G(d)(x, y; k, m, n), including several particular cases, are introduced and studied. Finally, a class of polynomials and corresponding numbers, obtained by a modification of the generating function of Humbert's polynomials, is also considered.

引用

页数：17

共 29 条

[1]

APOSTOL TM, 1951, B AM MATH SOC, V57, P370

[2] Some array type polynomials associated with special numbers and polynomials [J].