Askey–Gasper inequality

In mathematics, the Askey–Gasper inequality, named after Richard Askey and George Gasper, is an inequality for Jacobi polynomials proved by harvtxt|Askey|Gasper|1976. It states that if "β" ≥ 0, "α" + "β" ≥ −2, and −1 ≤ "x" ≤ 1 then

: $sum_{k=0}^n frac{P_k^{(alpha,eta)}(x)}{P_k^{(eta,alpha)}(1)} ge 0$

where

: $P_k^{(alpha,eta)}(x)$

is a Jacobi polynomial.

The case when β=0 and α is a non-negative integer was used by Louis de Branges in his proof of the Bieberbach conjecture.

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