Open AccessA NOTE ON BIGAUSSIAN PELL AND PELL-LUCAS NUMBERS
Author(s) -
Hasan Gökbaş
Publication year - 2021
Publication title -
journal of science and arts
Language(s) - English
Resource type - Journals
eISSN - 2068-3049
pISSN - 1844-9581
DOI - 10.46939/j.sci.arts-21.3-a07
Subject(s) - lucas number , lucas sequence , mathematics , catalan number , identity (music) , combinatorics , algebraic number , recurrence relation , algebra over a field , pure mathematics , fibonacci polynomials , fibonacci number , art , mathematical analysis , aesthetics , orthogonal polynomials , difference polynomials
In this study, we define a new type of Pell and Pell-Lucas numbers which are called biGaussian Pell and biGaussian Pell-Lucas numbers. We also give the relationship between negabiGaussian Pell and Pell-Lucas numbers and bicomplex Pell and Pell-Lucas numbers. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sums formulas for these new type numbers. Some algebraic proporties of biGaussian Pell and Pell-Lucas numbers which are connected between biGaussian numbers and Pell and Pell-Lucas numbers are investigated. Moreover, we give the matrix representation of biGaussian Pell and Pell-Lucas numbers.