Inequalities and bounds for generalized complete elliptic integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:373

Article

Neuman, Edward

关键词: Generalized complete elliptic integrals of the first and second kind;    Gauss hypergeometric function;    Power mean;    Logarithmic convexity;    Concavity/convexity;    Inequalities;    Lower and upper bounds;   

DOI  :  10.1016/j.jmaa.2010.06.060

来源: Elsevier

【 摘 要 】

Computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained. Also, bounds for some combinations and products for integrals under discussion are established. It has been proven that both families of integrals are logarithmically convex as functions of the first parameter. This property has been employed to obtain several inequalities involving integrals in question. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free