Askey–Gasperova nejednakost

U matematici, Askey–Gasperova nejednakost^[1], koja je dobila naziv po Richardu Askeyu i Georgeu Gasperu, je nejednakost za Jacobijeve polinome, koju su dokazali Askey i Gasper 1976. godine. Ona iskazuje da ako je β ≥ 0, α + β ≥ −2 i −1 ≤ x ≤ 1, tada je

${\displaystyle \sum _{k=0}^{n}{\frac {P_{k}^{(\alpha ,\beta )}(x)}{P_{k}^{(\beta ,\alpha )}(1)}}\geq 0}$

gdje je

${\displaystyle P_{k}^{(\alpha ,\beta )}(x)}$

Jacobijev polinom.

Slučaj kada je β=0 i α je nenegativni cijeli broj iskoristio je Louis de Branges u svom dokazu Bieberbachove konjekture.

Reference

1. Ekhad, Shalosh B. (1993-08-30). "A short, elementary, and easy, WZ proof of the Askey—Gasper inequality that was used by de Branges in his proof of the Bieberbach conjecture". Theoretical Computer Science. 117 (1): 199–202. doi:10.1016/0304-3975(93)90313-I. ISSN 0304-3975.

Vanjski linkovi

• Askey, Richard; Gasper, George (1976), "Positive Jacobi polynomial sums. II", American Journal of Mathematics, 98 (3): 709–737, ISSN 0002-9327, MR0430358