Sharp Bounds for the Ratio of Modified Bessel Functions

被引：15
|
作者：
Yang, Zhen-Hang [1 ,2 ]
Zheng, Shen-Zhou [1 ,3 ]
机构：
[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
[2] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, Peoples R China
[3] BCAM, Alameda Mazarredo 14, Bilbao 48009, Spain
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 04期
关键词：
Modified Bessel functions of the first kind of order nu; the ratio of modified Bessel functions; monotonicity; sharp bounds; INEQUALITIES; FORM; 1ST;
D O I：
10.1007/s00009-017-0971-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let I-nu(x) be the modified Bessel functions of the first kind of order nu, and S-p,S-nu(x) = W-nu(x)(2) - 2pW(nu)(x) - x(2) with W-nu(x) = xI(nu)(x)/I nu+1(x). We achieve necessary and sufficient conditions for the inequality Sp,(nu)(x) < u or S-p,S-nu(x) > l to hold for x > 0 by establishing the monotonicity of S-p,S-nu(x) in x is an element of (0, infinity) with nu > -3/2. In addition, the best parameters p and q are obtained to the inequality W-nu(x) (>) over bar )p + root x(2) + q(2) for x > 0. Our main achievements improve some known results, and it seems to answer an open problem recently posed by Hornik and Grun (J Math Anal Appl 408:91-101, 2013).
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页数：22
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