Difference between revisions of "Askey–Gasper inequality"
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Revision as of 23:55, 26 October 2011
In mathematics, the Askey–Gasper inequality is an inequality for Jacobi polynomials proved by Template:Harvs and used in the proof of the Bieberbach conjecture.
Statement
It states that if β ≥ 0, α + β ≥ −2, and −1 ≤ x ≤ 1 then
where
is a Jacobi polynomial.
The case when β=0 and α is a nonnegative integer was used by Louis de Branges in his proof of the Bieberbach conjecture.
The inequality can also be written as
Proof
Template:Harvs gave a short proof of this inequality, by combining the identity
with the Clausen inequality.
Generalizations
Template:Harvtxt give some generalizations of the Askey–Gasper inequality to basic hypergeometric series.
See also
References
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