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Fibonacci and Lucas differential equations. (English) Zbl 1406.11014

Summary: The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
34A30 Linear ordinary differential equations and systems
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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