Asymptotic behaviour of differentiated Bernstein polynomials
Heiner Gonska, Ioan Raşa (2009)
Matematički Vesnik
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Heiner Gonska, Ioan Raşa (2009)
Matematički Vesnik
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Qiang Wu (2003)
Journal de théorie des nombres de Bordeaux
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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. ...
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We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.
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