Recurrence relations with periodic coefficients and Chebyshev polynomials

Bernhard Beckermann; Jacek Gilewicz; Elie Leopold

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Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials. ...

Binomial coefficients.

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Reinhardt Euler, Luis H. Gallardo, Florian Luca (2014)

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In this paper, we study the properties of the sequence of polynomials given by $g_{0} = 0, g_{1} = 1$ , $g_{n + 1} = g_{n} + Δ g_{n - 1}$ for $n \geq 1$ , where $Δ \in 𝔽_{q} [t]$ is non-constant and the characteristic of $𝔽_{q}$ is $2$ . This complements some results from R. Euler, L.H. Gallardo: On explicit formulae and linear recurrent sequences, Acta Math. Univ. Comenianae, 80 (2011) 213-219.

Some properties of Noor integral operator of $(n + p - 1)$ -th order.

Aouf, M.K. (2009)

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