SOME RESULTS ON THE q-ANALOGUES OF THE INCOMPLETE FIBONACCI AND LUCAS POLYNOMIALS

Srivastava H. M., Tuğlu N., Cetin M.

MISKOLC MATHEMATICAL NOTES, cilt.20, ss.511-524, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.2832
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.511-524
  • Anahtar Kelimeler: Fibonacci polynomials and numbers, Lucas polynomials and numbers, q-Fibonacci polynomials, q-Lucas polynomials, incomplete Fibonacci numbers, incomplete Lucas numbers, equivalence of the q-analogues and the corresponding (p, q)-analogues, GENERALIZED FIBONACCI, NUMBERS
  • Gazi Üniversitesi Adresli: Evet

Özet

In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials F-n(k) (x, s, q) and the incomplete q-Lucas polynomials L-n(k) (x, s, q), respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the (p, q)-analogues (with 0 < q < p <= 1) by applying some obvious parametric variations, the additional parameter p being redundant.