INEQUALITIES FOR LEGENDRE FUNCTIONS AND GEGENBAUER FUNCTIONS

被引：17

作者：

LOHOFER, G

机构：

[1] Institut für Raumsimulation, Deutsche Forschungsanstalt für Luft- und Raumfahrt

来源：

JOURNAL OF APPROXIMATION THEORY | 1991年 / 64卷 / 02期

关键词：

D O I：

10.1016/0021-9045(91)90077-N

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper three new and simple bounds for the Legendre functions of the first kind Pv-μ(x) for real xε{lunate} [-1, 1] are proved. They can easily be transformed for an application to Gegenbauer functions. At first, a short summary of well-known inequalities of Pv-μ(x) is given. Then a bound is derived that seems to be completely new. Finally, improvements of two known inequalities are presented. © 1991.

引用

页码：226 / 234

页数：9

共 12 条

[1]

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

[2]

BERNSTEIN S, 1931, J MATH, V10, P219

[3] UNIFORM INEQUALITIES FOR ULTRASPHERICAL POLYNOMIALS AND BESSEL-FUNCTIONS OF FRACTIONAL ORDER [J].