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

  • Gulsah Ozdemir
  • Yilmaz Simsek
  • Gradimir V. MilovanovićEmail author
Article

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 \((x,y)\mapsto \mathbb {G}_{d}(x,y;k,m,n)\), 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.

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 

Mathematics Subject Classification

05A15 11B39 11B68 11B73 11B83 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Gulsah Ozdemir
    • 1
  • Yilmaz Simsek
    • 1
  • Gradimir V. Milovanović
    • 2
    • 3
    Email author
  1. 1.Department of Mathematics, Faculty of ScienceAkdeniz UniversityAntalyaTurkey
  2. 2.Serbian Academy of Sciences and ArtsBeogradSerbia
  3. 3.Faculty of Science and MathematicsUniversity of NišNišSerbia

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