On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials

Özkan E., Kuloǧlu B.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.14, sa.6, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 6
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s179355712150100x
  • Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: The new Narayana polynomials, Gauss Narayana numbers, Gauss Narayana polynomials
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal's triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal's triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.