Monotonicity and convexity involving generalized elliptic integral of the first kind

[1]  H. Alzer Inequalities for the beta function , 2014 .

[2]  Orhan Tuǧ On almost B-summable double sequence spaces , 2018, Journal of inequalities and applications.

[3]  Feng Qi (祁锋),et al.  Monotonicity of functions connected with the gamma function and the volume of the unit ball , 2012 .

[4]  Feng Qi (祁锋) Bounds for the Ratio of Two Gamma Functions , 2009 .

[5]  Matti Vuorinen,et al.  Generalized elliptic integrals and modular equations , 2000 .

[6]  Y. Chu,et al.  Sharp bounds for generalized elliptic integrals of the first kind , 2015 .

[7]  A note on inequalities for the ratio of zero-balanced hypergeometric functions , 2019, Proceedings of the American Mathematical Society, Series B.

[8]  Chao-Ping Chen Sharp inequalities and asymptotic series of a product related to the Euler–Mascheroni constant , 2016 .

[9]  Y. Chu,et al.  Approximation for the complete elliptic integral of the first kind , 2020 .

[10]  Zhen-Hang Yang,et al.  A positive answer to Bhatia—Li conjecture on the monotonicity for a new mean in its parameter , 2020 .

[11]  Matti Vuorinen,et al.  Some inequalitites for the growth of elliptic integrals , 1998 .

[12]  Huan Wang Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces , 2016, Journal of inequalities and applications.

[13]  Matti Vuorinen,et al.  Functional inequalities for hypergeometric functions and complete elliptic integrals , 1992 .

[14]  Feng Qi,et al.  A logarithmically completely monotonic function involving the ratio of two gamma functions and originating from the coding gain , 2013, ArXiv.

[15]  Árpád Baricz,et al.  Turán type inequalities for generalized complete elliptic integrals , 2007 .

[16]  Jingfeng Tian,et al.  Convexity and monotonicity for elliptic integrals of the first kind and applications , 2017, Applicable Analysis and Discrete Mathematics.

[17]  Y. Chu,et al.  A sharp double inequality involving generalized complete elliptic integral of the first kind , 2020 .

[18]  Horst Alzer,et al.  Some beta-function inequalities , 2003, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[19]  Zhen-Hang Yang,et al.  Monotonicity criterion for the quotient of power series with applications , 2015 .

[20]  Chao Chen Inequalities and asymptotic expansions for the psi function and the Euler–Mascheroni constant , 2016 .

[21]  Jing-Feng Tian,et al.  Sharp inequalities for the generalized elliptic integrals of the first kind , 2018, The Ramanujan Journal.

[22]  Yu-Ming Chu,et al.  On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind , 2018, Journal of Mathematical Analysis and Applications.

[23]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[24]  S. Qiu,et al.  Monotonicity properties and inequalities for the generalized elliptic integral of the first kind , 2019, Journal of Mathematical Analysis and Applications.

[25]  Tie-hong Zhao,et al.  Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function , 2020 .

[26]  P. Shiu,et al.  PI AND THE AGM A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advanced Texts) , 1988 .

[27]  Jackson B. Lackey,et al.  Errata: Handbook of mathematical functions with formulas, graphs, and mathematical tables (Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964) by Milton Abramowitz and Irene A. Stegun , 1977 .

[28]  Jing-Feng Tian,et al.  Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function , 2019, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas.