no. 8
Théorie des nombres
Monotonicity and sharp inequalities related to complete (p,q)-elliptic integrals of the first kind
Wang, Fei1  ; Qi, Feng2, 3, 4  
1 Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, Zhejiang, China
2 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
3 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
4 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China
Comptes Rendus. Mathématique, Tome 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
Wang, Fei 1 ; Qi, Feng 2, 3, 4

1 Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, Zhejiang, China
2 Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
3 School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
4 College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China 
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     title = {Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {961--970},
     publisher = {Acad\'emie des sciences, Paris},
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Wang, Fei; Qi, Feng. Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind. Comptes Rendus. Mathématique, Tome 358 (2020) no. 8, pp. 961-970. doi : 10.5802/crmath.119. http://www.numdam.org/articles/10.5802/crmath.119/

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