Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (5): 1269-1281.

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Concavity of the Complete p-Elliptic Integral of the Second Kind According to Hölder Mean

Miaokun Wang1(),Zaiyin He2(),Yuming Chu1,*()   

  1. 1 Department of Mathematics, Huzhou University, Zhejiang Huzhou 313000
    2 School of Mathematics, Hunan University, Hunan Changsha 410082
  • Received:2019-03-19 Online:2020-10-26 Published:2020-11-04
  • Contact: Yuming Chu E-mail:wmk000@126.com;hzy@zjhu.edu.cn;chuyuming@zjhu.edu.cn
  • Supported by:
    NSFC(11701176);NSFC(61373169)

Abstract:

In the article, we provide a necessary and sufficient condition such that the complete p-elliptic integral of the second kind is concave with respect to Hölder mean, which is a generalization of the previously known result on the complete elliptic integral of the second kind.

Key words: Complete p-elliptic integral, Generalized elliptic integral, Hölder mean, Concavity, Convexity

CLC Number: 

  • O174
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