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Fibonacci numbers and Legendre polynomials. (Chinese. English summary) Zbl 1009.11013

Let \(U_n(x)\) be the second type of Chebyshev polynomials with generation function \[ \sum_{n=0}^\infty U_n(x)t^n= \frac{1} {1-2xt+t^2}, \] and let \(P_n(x)\) be the Legendre polynomials with generating function \[ \sum_{n=0}^\infty P_n(x)t^n= \frac{1} {\sqrt{1-2xt+t^2}}. \] First the authors give a formula about the two kinds of polynomials and then establish several relations between the values of the Legendre polynomials.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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