Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials

Mustafa Asci and Esref Gurel
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 1, Pages 25–36
Full paper (PDF, 164 Kb)

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Authors and affiliations

Mustafa Asci
Department of Mathematics, Science and Arts Faculty
Pamukkale University, Kınıklı Denizli, Turkey
* Corresponding author

Esref Gurel
Department of Mathematics, Science and Arts Faculty
Pamukkale University, Kınıklı Denizli, Turkey

Abstract

In this study we define and study the Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials. We give generating function, Binet formula, explicit formula, Q matrix, determinantal representations and partial derivation of these polynomials. By defining these Gaussian polynomials for special cases GJ_n(1) is the Gaussian Jacobsthal numbers, Gj_n(1) is the Gaussian Jacobsthal Lucas numbers defined in [2].

Keywords

• Jacobsthal polynomials
• Jacobsthal Lucas polynomials
• Gaussian Fibonacci numbers

AMS Classification

• 11A07
• 11A41
• 11A51
• 11B50
• 11B65
• 11B75

References

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