[1] Alzer H, Richard K C. Series representation for special functions and mathematical constants. Ramanujan J, 2016, 40:291. https://doi.org/10.1007/s11139-015-9679-7
[2] Anderson G D, Qiu S-L, Vamanamurthy M K, Vuorinen M. Generalized elliptic integrals and modular equation. Pacific J Math, 2000, 192(1):1-37
[3] Anderson G D, Qiu S-L, Vamanamurthy M K, Vuorinen M. Conformal invariants, inequalities and quasiconformal Maps. J Wiley, 1997
[4] Baricz Á. Geometrically concave univariate distributions. J Math Anal Appl, 2010, 363(1):182-196
[5] Baricz Á. Turán type inequalities for hypergeometric functions. Proc Amer Math Soc, 2008, 136(9):3223-3229
[6] Baricz Á, Bhayo B A, Pogány T K. Functional inequalities for genera lized inverse trigonometric and hyperbolic functions. J Math Anal Appl, 2014, 417:244-259
[7] Baricz Á, Bhayo B A, Vuorinen M. Turán type inequalities for genera lized inverse trigonometric functions. Filomat, 2015, 19(2):303-313
[8] Baricz Á, Jankov D, Pogány T K. Turán type inequalities for Krätzel functions. J Math Anal Appl, 2012, 388(2):716-724
[9] Berndt B C, Bhargava S, Garvan F G. Ramanujan's theories of elliptic functions to alternative bases. Trans Amer Math Soc, 1995, 347(11):4163-4244
[10] Bhayo B A, Sándor J. Inequalities connecting generalized trigonometric functions with their inverses. Probl Anal Issues Anal, 2013, 20(2):82-90
[11] Bhayo B A, Vuorinen M. On generalized trigonometric functions with two parameters. J Approx Theory, 2012, 164:1415-1426
[12] Bhayo B A, Vuorinen M. Inequalities for eigenfunctions of the p-Laplacian. Issues of Analysis, 2013, 20(2):13-35
[13] Bhayo B A, Vuorinen M. On generalized complete elliptic integrals and modular functions. Proc Edinb Math Soc, 2012, 55:591-611
[14] Bushell P J, Edmunds D E, Remarks on generalised trigonometric functions. Rocky Mountain J Math, 2012, 42:13-52
[15] Wang M-K, Chu Y-M, Qiu S-L, Jiang Y-P. Convexity of the complete elliptic integrals of the first kind with respect to Hölder means. J Math Anal Appl, 2012, 388(2):1141-1146
[16] Drábek P, Manásevich R. On the closed solution to some p-Laplacian nonhomogeneous eigenvalue problems. Diff and Int Eqns, 1999, 12:723-740
[17] Edmunds D E, Gurka P, Lang J. Properties of generalized trigonometric functions. J Approx Theory, 2012, 164:47-56
[18] Heikkala V, Lindén H, Vamanamurthy M K, Vuorinen M. Generalized elliptic integrals and the Legendre M-function. J Math Anal Appl, 2008, 338:223-243. arXiv:math/0701438
[19] Huang T-R, Tan S-Y, Ma X-Y, Chu Y-M. Monotonicity properties and bounds for the complete p-elliptic integrals. J Inequal Appl, 2018, 2018. Article ID 239, 11 pages
[20] Kamiya T, Takeuchi S. Complete (p, q)-elliptic integrals with application to a family of means. J Classical Anal, 2017, 10(1):15-25. doi:10.7153/jca-10-02
[21] Lindqvist L. Some remarkable sine and cosine functions. Ricerche di Matematica, 1995, 44:269-290
[22] Neuman E. Some properties of the generalized Jacobian elliptic functions. Integral Transform Spec Funct, 2015, 26(7):498-506
[23] Neuman E. Inequalities for the generalized trigonometric, hyperbolic and Jacobian elliptic functions. J Math Inequal, 2015, 9(3):709-726
[24] Neuman E. Some properties of the generalized Jacobian elliptic functions Ⅱ. Integral Transforms Spec Funct, 2016, 27(2):101-110
[25] Neuman E. Some properties of the generalized Jacobian elliptic functions Ⅲ. Integral Transforms Spec Funct, 2016, 27(10):824-834
[26] Qian W-M, He Z-Y, Chu Y-M. Approximation for the complete elliptic integral of the first kind. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM, 2020, 114(2):Article ID 57, 12 pages. https://doi.org/10.1007/s13398-020-00784-9
[27] Slater L J. Generalized hypergeometric functions. Cambridge:Cambridge University Press, 1966
[28] Takeuchi S. Generalized Jacobian elliptic functions and their application to bifurcation problems associated with p-Laplacian. J Math Anal Appl, 2012, 385:24-35
[29] Takeuchi S. A new form of the generalized complete elliptic integrals. Kodai Math J, 2016, 39(1):202-226
[30] Takeuchi S. Legendre-type relations for generalized complete elliptic integrals. J Classical Anal, 2016, 9(1):35-42. doi:10.7153/jca-09-04
[31] Wang M-K, Chu H-H, Chu Y-M. Precise bounds for the weighted Hölder mean of the complete p-elliptic integrals. J Math Anal Appl, 2019, 480(2):Article ID 123388, 9 pages
[32] Wang M-K, Chu Y-M, Qiu Y-F, Qiu S-L. An optimal power mean inequality for the complete elliptic integrals. Appl Math Lett, 2011, 24(6):887-890
[33] Wang M-K, He Z-Y, Chu Y-M. Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind. Comput Methods Funct Theory, 2020, 20(1):111-124
[34] Wang M-K, Hong M-Y, Xu Y-F, et al. Inequalities for generalized trigonometric and hyperbolic functions with one parameter. J Math Inequal, 2020, 14(1):1-21
[35] Wang M-K, Qiu S-L, Chu Y-M, Jiang Y-P. Generalized Hersch-Pfluger distortion function and complete elliptic integrals. J Math Anal Appl, 2012, 385(1):221-229
[36] Wang G-D, Zhang X-H, Chu Y-M. A power mean inequality involving the complete elliptic integrals. Rocky Mountain J Math, 2014, 44(5):1661-1667
[37] Wang M-K, Zhang W, Chu Y-M. Monotonicity, convexity and inequalities involving the generalized elliptic integrals. Acta Mathematica Scientia, 2019, 39B(5):1440-1450
[38] Yang Z-H, Chu Y-M. A monotonicity property involving the generalized elliptic integral of the first kind. Math Inequal Appl, 2017, 20(3):729-735
[39] Yang Z-H, Qian W-M, Chu Y-M, Zhang W. On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind. J Math Anal Appl, 2018, 462(2):1714-1726
[40] Yang Z-H, Qian W-M, Zhang W, Chu Y-M. Notes on the complete elliptic integral of the first kind. Math Inequal Appl, 2020, 23(1):77-93
[41] Yang Z-H, Qian W-M, Chu Y-M. Monotonicity properties and bounds involving the complete elliptic integrals of the first kind. Math Inequal Appl, 2018, 21(4):1185-1199
[42] Yin L, Huang L-G, Lin X-L, Wang Y-L. A survey for generalized trigonometric and hyperbolic functions. J Math Inequal, 2019, 13(3):833-854 |