Bernstein’s inequality for Jacobi polynomials P (α,β) n , established in 1987 by P. Baratella for the regionR1/2 = {|α| ≤ 1/2, |β| ≤ 1/2}, and subsequently supplied with an improved constant by Y. C how, L. Gatteschi, and R. Wong, is analyzed here analytically and , bove all, computationally with regard to validity and sharpness, not only in the original region R1/2, but also in larger regions Rs = {−1/2 ≤ α ≤ s,−1/2 ≤ β ≤ s}, s > 1/2. Computation suggests that the inequality holds with new, s… CONTINUE READING

Inequalities for ultraspherical polynomials and th e gamma function

L ORCH, LEE

J. Approx. Theory • 1984

Alternative proof of a sharpened form of Bernstei n’s inequality for Legendre polynomials

L ORCH, LEE

Applicable Anal. 14 (no • 1982

Estimation of a remainder of a Legendre polynomial generating function expansion (generalizatio n and refinement of the Bernšteı̆n inequality (Russian), Vestnik Leningrad