In this paper, new formulas for the Fibonacci polynomials, including high-order derivatives and repeated integrals of them, are derived in terms of the polynomials themselves. The results are then used to solve connection problems between the Fibonacci and orthogonal polynomials. The inverse cases are also studied. Finally, new results for the linear products of the Fibonacci and orthogonal polynomials are determined using the earlier result for the moments formula of Fibonacci polynomials.

New Formulas Involving Fibonacci and Certain Orthogonal Polynomials

Napoli A.
;
2023-01-01

Abstract

In this paper, new formulas for the Fibonacci polynomials, including high-order derivatives and repeated integrals of them, are derived in terms of the polynomials themselves. The results are then used to solve connection problems between the Fibonacci and orthogonal polynomials. The inverse cases are also studied. Finally, new results for the linear products of the Fibonacci and orthogonal polynomials are determined using the earlier result for the moments formula of Fibonacci polynomials.
2023
Fibonacci polynomials
high-order derivatives
linearization and connection coefficients
orthogonal polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/376918
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