Inequalities and monotonicity properties for the gamma function

被引：25

作者：

Giordano, C

Laforgia, A

机构：

[1] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

[2] Univ Roma Tre, Dipartimento Matemat, Rome, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2001年 / 133卷 / 1-2期

关键词：

gamma function; inequality; ultraspherical polynomials;

D O I：

10.1016/S0377-0427(00)00659-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a survey of some recent results on the ratio of two gamma functions and prove the following inequalities for the product: 1/2 r(1 + x(1) + x(2)) less than or equal to r(1 + x(1))r(1 + x(2)) < r(1 + x(1) + x(2)) for x(1),x(2) > 0 and x(1).x(2) = 1. Finally, we study the possible extension to k variables of the lower bound above. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：387 / 396

页数：10

共 25 条

[1] On some inequalities for the gamma and psi functions [J].