Article ID Journal Published Year Pages File Type
4615713 Journal of Mathematical Analysis and Applications 2014 9 Pages PDF
Abstract
A recent conjecture by I. Raşa asserts that the sum of the squared Bernstein basis polynomials is a convex function in [0,1]. This conjecture turns out to be equivalent to a certain upper pointwise estimate of the ratio Pn′(x)/Pn(x) for x≥1, where Pn is the n-th Legendre polynomial. Here, we prove both upper and lower pointwise estimates for the ratios (Pn(λ)(x))′/Pn(λ)(x), x≥1, where Pn(λ) is the n-th ultraspherical polynomial. In particular, we validate Raşa's conjecture.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
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