Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials
SIAM Journal on Mathematical Analysis - Special issue: the articles in this issue are dedicated to Richard Askey and Frank Olver
Bounds for orthogonal polynomials for exponential weights
Journal of Computational and Applied Mathematics
A new bound for the Laguerre polynomials
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
On the Bernstein-type inequalities for ultraspherical polynomials
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials
Advances in Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On extreme zeros of classical orthogonal polynomials
Journal of Computational and Applied Mathematics
Inequalities for orthonormal Laguerre polynomials
Journal of Approximation Theory
An upper bound on Jacobi polynomials
Journal of Approximation Theory
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A remarkable inequalily, with utterly explicit constants, established by Erdélyi, Magnus, and Nevai, states that for x ≥ β -1/2, the orthonormal Jacobi polynomials Pk(x,β)(x) satisfy max|x|≤1 {(1 - x)α+1/2(1+x)β+1/2(Pk(α,β)(x))2} = O(α) [Erdélyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994), 602 614]. They conjectured that the real order of the maximum is O(x1/2). Here we will make half a way towards this conjecture by proving a new inequality which improves their result by a factor of order {1/x + 1/k)-1/3. We also confirm the conjecture, even in a stronger form, in some limiting cases.