On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials
Date
2007ISSN
1017-1398Source
Numerical AlgorithmsVolume
44Issue
3Pages
249-253Google Scholar check
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Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality (equation presented) holds for α, β > - 1 and n ≥ 1, θ∈ ∈(0, π), where Pn(α,β)(x) are the Jacobi polynomials of degree n and parameters (α, β). We settle this conjecture in the special cases where (α, β) ∈ {(1/2,1/2), (1/2,-1/2), (-1/2,1/2}}. © 2007 Springer Science+Business Media LLC.