Concavity and bounds involving generalized elliptic integral of the first kind

By Tie-hong Zhao, Miao-Kun Wang, Yuming Chu. Journal of Mathematical Inequalities, 2021

162 citations recorded by the source corpus.

. In the article, we provide a suf fi cient condition for value range of the constant c such that the function x → K a ( √ x ) / log ( c / √ 1 − x ) is strictly concave on ( 0 , 1 ) for a ∈ ( 0 , 1 / 2 ] , which generalize a very recently obtained result that the function x → K ( √ x ) / log ( c / √ 1 − x ) is strictly concave on ( 0 , 1 ) if and only if c = e 4 / 3 . As applications, we present new bounds for K a ( x ) , K a ( √ 1 − x 2 ) / K a ( √ x ) and K a ( √ 1 − x 2 ) K a ( √ x ) , where K a ( x ) is the generalized elliptic integral of the fi rst kind and K ( x ) = K 1 / 2 ( x ) .

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/d737c050d509b2a7d7307b3c6e615d0771894b97

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

  1. Tie-hong Zhao
  2. Y. Chu
  3. Zhonghua Shen
  4. Miao-Kun Wang
  5. Wei-Mao Qian
  6. Saima Rashid
  7. M. Adil Khan
  8. Muhammad Aslam Noor

Citations in the corpus