Landen-Type Inequality for Bessel Functions

被引：2

作者：

Árpád Baricz

机构：

[1] Babeş-Bolyai University,Faculty of Mathematics and Computer Science

来源：

Computational Methods and Function Theory | 2006年 / 5卷 / 2期

关键词：

Landen inequality; hypergeometric functions; Bessel functions; Kummer functions; 33C05; 33C10; 33C15;

D O I：

10.1007/BF03321104

中图分类号：

学科分类号：

摘要：

Let up(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let λ(r) = up(r2), r ∈} (0,1). Motivated by an open problem of Anderson, Vamanamurthy and Vuorinen, we prove that the Landen-type inequality λ(2√r/(1 + r)) < Cλ(r) holds for all r ∈ (0,1) and C > 1, for certain conditions on the parameters b,c,p.

引用

页码：373 / 379

页数：6

共 6 条

[1]

Almkvist G(1988)Gauss, Landen Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies Diary, Amer. Math. Monthly 95 585-608

[2]

Berndt B(1997)Asymptotic expansions and inequalities for hypergeometric functions Mathematika 44 43-64

[3]

Ponnusamy S(1999)Landen inequalities for hypergeometric functions Nagoya Math. J. 154 31-56

[4]

Vuorinen M(undefined)undefined undefined undefined undefined-undefined

[5]

Qiu S L(undefined)undefined undefined undefined undefined-undefined

[6]

Vuorinen M(undefined)undefined undefined undefined undefined-undefined

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