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

OZDEMIR G., ŞİMŞEK Y., MILOVANOVIC G. V.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.14, no.3, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s00009-017-0918-6
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: 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
  • Akdeniz University Affiliated: Yes

Abstract

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.