Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615713 | Journal of Mathematical Analysis and Applications | 2014 | 9 Pages |
Abstract
A recent conjecture by I. RaÅa 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 Pnâ²(x)/Pn(x) for xâ¥1, where Pn is the n-th Legendre polynomial. Here, we prove both upper and lower pointwise estimates for the ratios (Pn(λ)(x))â²/Pn(λ)(x), xâ¥1, where Pn(λ) is the n-th ultraspherical polynomial. In particular, we validate RaÅa's conjecture.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Geno Nikolov,