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Generalized Vieta-Jacobsthal and Vieta-Jacobsthal-Lucas polynomials. (English) Zbl 1355.11016

Summary: In this paper, generalized Vieta-Jacobsthal and Vieta-Jacobsthal-Lucas polynomials are introduced. The Binet form and some of their recursive features are given. Various families of multilinear and multilateral generating functions for these polynomials are derived. Furthermore, some special cases of the results are presented in this study.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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