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, cilt.13, sa.2, ss.478-494, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/aadm180215016k
  • Dergi Adı: APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.478-494
  • Anahtar Kelimeler: Generating functions, Computation algorithm, Apostol-type numbers and polynomials, Stirling numbers, Combinatorial numbers, EULER, BERNOULLI
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.