New Computational Formulas for Special Numbers and Polynomials Derived from Applying Trigonometric Functions to Generating Functions

Kilar N., ŞİMŞEK Y.

MILAN JOURNAL OF MATHEMATICS, vol.89, no.1, pp.217-239, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 89 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s00032-021-00333-y
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.217-239
  • Keywords: Bernoulli numbers and polynomials, Euler numbers and polynomials, Stirling numbers, Cosine-type Bernoulli and Euler polynomials, Sine-type Bernoulli and Euler polynomials, Trigonometric and generating functions, COMBINATORIAL SUMS, EULER, BERNOULLI, IDENTITIES
  • Akdeniz University Affiliated: Yes


The aim of this paper is to apply trigonometric functions with functional equations of generating functions. Using the resulted new equations and formulas from this application, we obtain many special numbers and polynomials such as the Stirling numbers, Bernoulli and Euler type numbers, the array polynomials, the Catalan numbers, and the central factorial numbers. We then introduce combinatorial sums related to these special numbers and polynomials. Moreover, we gave some remarks that relates our new findings from this paper to the relations found in earlier studies.