Catalan transform of the k-Pell, k-Pell–Lucas and modified k-Pell sequence
Merve Taştan, Engi̇n Özkan
Abstract
In this study, we present the Catalan transforms of the k-Pell sequence, the k-Pell–Lucas sequence and the Modified k-Pell sequence and examine the properties of the sequences. Then we apply the Hankel transform to the Catalan transforms of the k-Pell sequence, the Catalan transform of the k-Pell–Lucas sequence and the Catalan transform of the Modified k-Pell sequence. Also, we obtain the generating functions of the Catalan transform of the k-Pell sequence, k-Pell–Lucas sequence and Modified k-Pell sequence. Furthermore, we acquire an interesting characteristic related to the determinant of the Hankel transform of the sequences.
Topics & Concepts
CatalanCatalan numberSequence (biology)MathematicsLucas sequenceCombinatoricsHankel transformMathematical analysisFourier transformPhilosophyChemistryLinguisticsFibonacci polynomialsOrthogonal polynomialsBiochemistryDifference polynomialsAdvanced Mathematical Theories and ApplicationsFractal and DNA sequence analysisAdvanced Mathematical Identities