ON A FAMILY OF SPECIAL NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-TYPE NUMBERS AND POYNOMIALS AND COMBINATORIAL NUMBERS


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KÜÇÜKOĞLU İ., ŞİMŞEK Y.

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, vol.13, no.2, pp.478-494, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.2298/aadm180215016k
  • Journal Name: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.478-494
  • Keywords: Generating functions, Computation algorithm, Apostol-type numbers and polynomials, Stirling numbers, Combinatorial numbers, EULER, BERNOULLI
  • Akdeniz University Affiliated: Yes

Abstract

In this article, we examine a family of some special numbers and polynomials not only with their generating functions, but also with computation algorithms for these numbers and polynomials. By using these algorithms, we provide several values of these numbers and polynomials. Furthermore, some new identities, formulas and combinatorial sums are obtained by using relations derived from the functional equations of these generating functions. These identities and formulas include the Apostol-type numbers and polynomials, and also the Stirling numbers. Finally, we give further remarks and observations on the generating function including lambda-Apostol-Daehee numbers, special numbers, and finite sums.