A Bernstein–Type Inequality for the Jacobi Polynomial

Abstract:

Let be the Jacobi polynomial of degree n. For and 0 ≤ θ ≤ π , it is proved that

where q = max(α, β) and . When α = β = 0, this reduces to a sharpened form of the weH-kno..,n Bernstein inequality for the Legendre polynomial