Then, we get Cassini’s identities for these numbers and polynomials.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers.
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Key Findings & Data:We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers.
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Conclusion & Impact:Then, we get Cassini’s identities for these numbers and polynomials.
In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.
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