Certain Combinatorial Properties of Twin Triplets Related to Tchebychev Polynomials
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Keywords:
Combinatorial Identities, Continued fractions, Functions of hypergeometric type in one and severable variablesAbstract
In the present paper, Tchebychev polynomials $U_{n}(x)$, $V_{n}(x)=U_{n}(x)-\,U_{n-1}(x)$ and $W_{n}(x)=U_{n}(x)+\,U_{n-1}(x)$ are extended to two variables. Twin triplets of numbers $(y_{n},d_{n},s_{n})$ and $(Y_{n},D_{n},S_{n})$ are defined and their certain combinatorial properties are described.
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