A BERNSTEIN-TYPE INEQUALITY FOR THE JACOBI POLYNOMIAL

被引：21

作者：

CHOW, YY

GATTESCHI, L

WONG, R

机构：

[1] UNIV TURIN, DEPT MATH, I-10124 TURIN, ITALY

[2] UNIV MANITOBA, DEPT APPL MATH, WINNIPEG R3T 2N2, MANITOBA, CANADA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 121卷 / 03期

关键词：

JACOBI POLYNOMIAL; BERNSTEIN INEQUALITY; HYPERGEOMETRIC FUNCTION;

D O I：

10.2307/2160265

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P(n)(alpha, beta)(x) be the Jacobi polynomial of degree n. For -1/2 less-than-or-equal-to alpha, beta less-than-or-equal-to 1/2 and 0 less-than-or-equal-to theta less-than-or-equal-to pi, it is proved that (sin theta/2)alpha+1/2(cos theta/2)beta+1/2\P(n)(alpha, beta)(cos theta)\less-than-or-equal-to GAMMA(q + 1)/GAMMA(1/2)(n+q/n)N(-q-1/2), where q = max(alpha, beta) and N = n + 1/2(alpha + beta + 1) . When alpha = beta = 0, this reduces to a sharpened form of the well-known Bernstein inequality for the Legendre polynomial.

引用

页码：703 / 709

页数：7

共 9 条

[1]

Antonov V. A., 1981, VESTNIK LENINGRAD U, V13, P163

[2]

BARATELLA P, 1986, ATTI ACCAD SCI SFMN, V120, P207

[3]

Durand L., 1975, THEORY APPL SPECIAL, P353

[4]

GASPER G, FRACTIONAL CALCULUS, V457, P207