Two Parametric Kinds of Eulerian-Type Polynomials Associated with Euler's Formula

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Kilar N., ŞİMŞEK Y.

SYMMETRY-BASEL, vol.11, no.9, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 9
  • Publication Date: 2019
  • Doi Number: 10.3390/sym11091097
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Apostol-type numbers and polynomials, Stirling numbers, combinatorial sum, generating function, special functions, GENERATING-FUNCTIONS, BERNOULLI NUMBERS, APOSTOL, IDENTITIES
  • Akdeniz University Affiliated: Yes


The purpose of this article is to construct generating functions for new families of special polynomials including two parametric kinds of Eulerian-type polynomials. Some fundamental properties of these functions are given. By using these generating functions and the Euler's formula, some identities and relations among trigonometric functions, two parametric kinds of Eulerian-type polynomials, Apostol-type polynomials, the Stirling numbers and Fubini-type polynomials are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.