A Q-ANALOG OF THE BI-PERIODIC LUCAS SEQUENCE

Tan E.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.67, sa.2, ss.220-228, 2018 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1501/commua1_0000000876
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.220-228
  • Anahtar Kelimeler: bi-periodic Fibonacci and Lucas sequences, bi-periodic incomplete Fibonacci and Lucas sequences, q-analog, matrix formula, CONDITIONAL SEQUENCES, MATRIX-METHOD, FIBONACCI, POLYNOMIALS, IDENTITIES, NUMBERS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formulas for the q-bi-periodic Fibonacci and Lucas sequences, we introduce q-analogs of the bi-periodic incomplete Fibonacci and Lucas sequences and give a relation between them.