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Askey–Gasper inequality : ウィキペディア英語版
Askey–Gasper inequality
In mathematics, the Askey–Gasper inequality is an inequality for Jacobi polynomials proved by and used in the proof of the Bieberbach conjecture.
==Statement==
It states that if , and then
:\sum_^n \frac \ge 0
where
:P_k^(x)
is a Jacobi polynomial.
The case when can also be written as
:(\alpha+1);\tfrac(\alpha+3),\alpha+1;t \right)>0, \qquad 0\leq t<1, \quad \alpha>-1.
In this form, with a non-negative integer, the inequality was used by Louis de Branges in his proof of the Bieberbach conjecture.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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