Binomial Transforms of the Third-Order Jacobsthal and Modified Third-Order Jacobsthal Polynomials
Abstract
In this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations. Also, we establish the relations between these transforms by deriving new formulas. Finally, the Vajda, d'Ocagne, Catalan and Cassini formulas for these transforms are obtained.
Keywords
Binomial transforms, Modified third-order Jacobsthal numbers, Third-order Jacobsthal numbers, Third-order Jacobsthal polynomials
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