Askey–Gasper inequality

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.

References

*Citation | author1-link=Richard Askey | last1=Askey | first1=Richard | last2=Gasper | first2=George | title=Positive Jacobi polynomial sums. II | url=http://www.jstor.org/stable/2373813 | id=MathSciNet | id = 0430358 | year=1976 | journal=American Journal of Mathematics | issn=0002-9327 | volume=98 | issue=3 | pages=709–737


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • de Branges's theorem — In complex analysis, the Bieberbach conjecture or de Branges s theorem, posed by Ludwig Bieberbach (1916) and proven by Louis de Branges (1985), states a necessary condition on a holomorphic function to map the open unit disk of the… …   Wikipedia

  • Bieberbach conjecture — In complex analysis, the Bieberbach conjecture or de Branges s theorem, asked by harvs|txt|first=Ludwig |last=Bieberbach|authorlink=Ludwig Bieberbach|year=1916 and proved by harvs|txt|authorlink=Louis de Branges de Bourcia|first=Louis |last=de… …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • List of inequalities — This page lists Wikipedia articles about named mathematical inequalities. Inequalities in pure mathematics =Analysis= * Askey–Gasper inequality * Bernoulli s inequality * Bernstein s inequality (mathematical analysis) * Bessel s inequality *… …   Wikipedia

  • Clausen's formula — In mathematics, Clausen s formula, found by Thomas Clausen (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states In particular it gives conditions for a hypergeometric series to be …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”