Fibonacci numbers and orthogonal polynomials
نویسنده
چکیده
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, 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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