Comptes Rendus
no. 8
Théorie des nombres
Monotonicity and sharp inequalities related to complete (p,q)-elliptic integrals of the first kind
Fei Wang1  ; Feng Qi2, 3, 4  
1 Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, Zhejiang, China
2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
3 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
4 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 961-970.

With the aid of the monotone L’Hôpital rule, the authors verify monotonicity of some functions involving complete (p,q)-elliptic integrals of the first kind and the inverse of generalized hyperbolic tangent function, derive several sharp inequalities of complete (p,q)-elliptic integrals of the first kind, and generalize some known sharp approximation of complete elliptic integrals of the first kind.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.119
Classification : 33E05, 33C75

Fei Wang 1 ; Feng Qi 2, 3, 4

1 Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, Zhejiang, China
2 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
3 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
4 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Fei Wang; Feng Qi. Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 961-970. doi : 10.5802/crmath.119. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.119/

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