Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

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Wang Y., DAĞLI M. C., Liu X., Qi F.

AXIOMS, cilt.10, sa.1, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3390/axioms10010037
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Faa di Bruno formula, generalized Eulerian polynomial, Bell polynomial of the second kind, general formula for derivatives of the ratio between two differentiable functions, explicit formula, determinantal formula, recurrent formula, Stirling number of the second kind
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In the paper, by virtue of the Faa di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.