Fibonacci numbers and orthogonal polynomials | Zendy

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Fibonacci numbers and orthogonal polynomials

Author(s) -

Christian Berg

Publication year - 2011

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2011.01.001

Subject(s) - mathematics , orthogonal polynomials , discrete orthogonal polynomials , classical orthogonal polynomials , fibonacci polynomials , fibonacci number , combinatorics , integer sequence , wilson polynomials , hahn polynomials , sequence (biology) , integer (computer science) , inverse , recurrence relation , discrete mathematics , difference polynomials , gegenbauer polynomials , hankel matrix , mathematical analysis , generating function , geometry , biology , computer science , genetics , programming language

We prove that the sequence (1/Fn+2)n⩾0 of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability measure and we identify the orthogonal polynomials as little q-Jacobi polynomials with q=1-5/1+5. We prove that the corresponding kernel polynomials have integer coefficients, and from this we deduce that the inverse of the corresponding Hankel matrices (1/Fi+j+2) have integer entries. We prove analogous results for the Hilbert matrices

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